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University Physics with Modern Physics

Hugh D. Young

Chapter 21

Electric Charge and Electric Field - all with Video Answers

Educators

+ 24 more educators

Chapter Questions

04:18

Problem 1

Excess electrons are placed on a small lead sphere with mass 8.00 g so that its net charge is -3.20 x 10$^{-9}$C. (a) Find the number of excess electrons on the sphere. (b) How many excess electrons are there per lead atom? The atomic number of lead is 82, and its atomic mass is 207 g/mol.

Vishal Gupta
Vishal Gupta
Numerade Educator
02:26

Problem 2

Lightning occurs when there is a flow of electric charge (principally electrons) between the ground and a thundercloud. The maximum rate of charge flow in a lightning bolt is about
20,000 C$/$s; this lasts for 100 $\mu$s or less. How much charge flows between the ground and the cloud in this time? How many electrons flow during this time?

Vishal Gupta
Vishal Gupta
Numerade Educator
05:03

Problem 3

If a proton and an electron are released when they are 2.0 x 10$^{-10}$ m apart (a typical atomic distance), find the initial acceleration of each particle.

Rachel Wellington
Rachel Wellington
University of Georgia
15:35

Problem 4

You have a pure (24-karat) gold ring of mass 10.8 g. Gold has an atomic mass of 197 g$/$mol and an atomic number of 79. (a) How many protons are in the ring, and what is their total positive charge? (b) If the ring carries no net charge, how many electrons are in it?

DL
Daniel Lebrun
George Mason University
03:18

Problem 5

$Neurons$ are components of the nervous system of the body that transmit signals as electric impulses travel along their length. These impulses propagate when charge suddenly rushes into and then out of a part of the neuron called an axon. Measurements have shown that, during the inflow part of this cycle, approximately 5.6 x $10^{11}$ Na$^{+}$ (sodium ions) per meter, each with charge $+e$, enter the axon. How many coulombs of charge enter a 1.5-cm length of the axon during this process?

Averell Hause
Averell Hause
Carnegie Mellon University
16:20

Problem 6

Two small spheres spaced 20.0 cm apart have equal charge. How many excess electrons must be present on each sphere if the magnitude of the force of repulsion between them is
3.33 $\times$ $10^{-21}$ N?

DL
Daniel Lebrun
George Mason University
02:18

Problem 7

An average human weighs about 650 N. If each of two average humans could carry 1.0 C of excess charge, one positive and one negative, how far apart would they have to be for the electric attraction between them to equal their 650-N weight?

Rachel Wellington
Rachel Wellington
University of Georgia
03:03

Problem 8

Two small aluminum spheres, each having mass 0.0250 kg, are separated by 80.0 cm. (a) How many electrons does each sphere contain? (The atomic mass of aluminum is 26.982 g$/$mol, and its atomic number is 13.) (b) How many electrons would have to be removed from one sphere and added to the other to cause an attractive force between the spheres of magnitude 1.00 $\times$ 10$^4$ N (roughly 1 ton)? Assume that the spheres may be treated as point charges. (c) What fraction of all the electrons in each sphere does this represent?

Anand Jangid
Anand Jangid
Numerade Educator
06:27

Problem 9

Two small plastic spheres are given positive electric charges. When they are 15.0 cm apart, the repulsive force between them has magnitude 0.220 N. What is the charge on each sphere (a) if the two charges are equal and (b) if one sphere has four times the charge of the other?

Rachel Wellington
Rachel Wellington
University of Georgia
31:03

Problem 10

Suppose you had two small boxes, each containing 1.0 g of protons. (a) If one were placed on the moon by an astronaut and the other were left on the earth, and if they were connected by a very light (and very long!) string, what would be the tension in the string? Express your answer in newtons and in pounds. Do you need to take into account the gravitational forces of the earth and moon on the protons? Why? (b) What gravitational force would each box of protons exert on the other box?

Paul A.
Paul A.
California State Polytechnic University, Pomona
06:50

Problem 11

In an experiment in space, one proton is held fixed and another proton is released from rest a distance of 2.50 mm away. (a) What is the initial acceleration of the proton after it is released? (b) Sketch qualitative (no numbers!) acceleration-time and velocity-time graphs of the released proton's motion.

Rachel Wellington
Rachel Wellington
University of Georgia
11:24

Problem 12

A negative charge of $-0.550 \space \mu$C exerts an upward 0.600-N force on an unknown charge that is located 0.300 m directly below the first charge. What are (a) the value of the unknown charge (magnitude and sign); (b) the magnitude and direction of the force that the unknown charge exerts on the $-$0.550-$\mu$C charge?

DL
Daniel Lebrun
George Mason University
05:23

Problem 13

Three point charges are arranged on a line. Charge $q_3 = +$5.00 nC and is at the origin. Charge $q_2 = -$3.00 nC and is at $x = +$4.00 cm. Charge $q_1$ is at $x = +$2.00 cm. What is $q_1$ (magnitude and sign) if the net force on $q_3$ is zero?

Rachel Wellington
Rachel Wellington
University of Georgia
28:30

Problem 14

In Example 21.4, suppose the point charge on the y-axis at $y = -$0.30 m has negative charge $-2.0 \space \mu$C, and the other charges remain the same. Find the magnitude and direction of the net force on Q. How does your answer differ from that in Example 21.4? Explain the differences.

DL
Daniel Lebrun
George Mason University
05:40

Problem 15

In Example 21.3, calculate the net force on charge $q_1$ .

Rachel Wellington
Rachel Wellington
University of Georgia
03:16

Problem 16

In Example 21.4, what is the net force (magnitude and direction) on charge $q_1$ exerted by the other two charges?

Ze-Han Lee
Ze-Han Lee
Numerade Educator
05:49

Problem 17

Three point charges are arranged along the $x$-axis. Charge $q_1 = +3.00 \space \mu$C is at the origin, and charge $q_2 = -5.00 \space \mu$C is at $x =$ 0.200 m. Charge $q_3 = -8.00 \space \mu$C. Where is $q_3$ located if the net force on $q_1$ is 7.00 N in the $-$ $x$-direction ?

Rachel Wellington
Rachel Wellington
University of Georgia
05:17

Problem 18

Repeat Exercise 21.17 for $q_3 = +8.00 \space \mu$C.

Ze-Han Lee
Ze-Han Lee
Numerade Educator
05:16

Problem 19

Two point charges are located on the $y$-axis as follows: charge $q_1 = -1.50 $nC at $y = -$0.600 m, and charge $q_2 = +$3.20 nC at the origin $(y = 0)$. What is the total force (magnitude and direction) exerted by these two charges on a third charge $q_3 = +$5.00 nC located at $y = -$0.400 m ?

Rachel Wellington
Rachel Wellington
University of Georgia
01:43

Problem 20

Two point charges are placed on the $x$-axis as follows: Charge $q_1 = +$4.00 nC is located at $x =$ 0.200 m, and charge $q_2 = +$5.00 nC is at $x = -$0.300 m . What are the magnitude and direction of the total force exerted by these two charges on a negative point charge $q_3 = -$6.00 nC that is placed at the origin?

Ze-Han Lee
Ze-Han Lee
Numerade Educator
10:28

Problem 21

The two sides of the DNA double helix are connected by pairs of bases (adenine, thymine, cytosine, and guanine). Because of the geometric shape of these molecules, adenine bonds with thymine and cytosine bonds with guanine. $\textbf{Figure E21.21}$ shows the bonding of thymine and adenine. Each charge shown is $\pm e$, and the H$-$N distance is 0.110 nm. (a) Calculate the $net$ force that thymine exerts on adenine. Is it attractive or repulsive? To keep the calculations fairly simple, yet reasonable, consider only the forces due to the O$-$H$-$N and the N$-$H$-$N combinations, assuming that these two combinations are parallel to each other. Remember, however, that in the O$-$H$-$N set, the O$^-$ exerts a force on both the H$^+$ and the N$^-$, and likewise along the N$-$H$-$N set. (b) Calculate the force on the electron in the hydrogen atom, which is 0.0529 nm from the proton. Then compare the strength of the bonding force of the electron in hydrogen with the bonding force of the adenine-thymine molecules.

Rachel Wellington
Rachel Wellington
University of Georgia
03:34

Problem 22

Refer to Exercise 21.21. $\textbf{Figure E21.22}$ shows the bonding of cytosine and guanine. The O$-$H and H$-$N distances are each 0.110 nm. In this case, assume that the bonding is due only to the forces along the O$-$H$-$O, N$-$H$-$N, and O$-$H$-$N combinations, and assume also that these three combinations are parallel to each other. Calculate the net force that cytosine exerts on guanine due to the preceding three combinations. Is this force attractive or repulsive?

Ummatul Choudary
Ummatul Choudary
Numerade Educator
03:24

Problem 23

A proton is placed in a uniform electric field of 2.75 $\times 10^3 \space N/C$. Calculate (a) the magnitude of the electric force felt by the proton; (b) the proton's acceleration; (c) the proton's speed after 1.00 $\mu$s in the field, assuming it starts from rest.

Vishal Gupta
Vishal Gupta
Numerade Educator
02:19

Problem 24

A particle has charge $-$5.00 nC. (a) Find the magnitude and direction of the electric field due to this particle at a point 0.250 m directly above it. (b) At what distance from this particle does its electric field have a magnitude of 12.0 N$/$C?

Ze-Han Lee
Ze-Han Lee
Numerade Educator
09:40

Problem 25

A proton is traveling horizontally to the right at 4.50 $\times 10^6$ m$/$s. (a) Find the magnitude and direction of the weakest electric field that can bring the proton uniformly to rest over a distance of 3.20 cm. (b) How much time does it take the proton to stop after entering the field? (c) What minimum field (magnitude and direction) would be needed to stop an electron under the conditions of part (a)?

Rachel Wellington
Rachel Wellington
University of Georgia
02:50

Problem 26

An electron is released from rest in a uniform electric field. The electron accelerates vertically upward, traveling 4.50 m in the first 3.00 $\mu$s after it is released. (a) What are the magnitude and direction of the electric field? (b) Are we justified in ignoring the effects of gravity? Justify your answer quantitatively.

Ze-Han Lee
Ze-Han Lee
Numerade Educator
03:12

Problem 27

(a) What must the charge (sign and magnitude) of a 1.45-g particle be for it to remain stationary when placed in a downward-directed electric field of magnitude 650 N$/$C? (b) What is the magnitude of an electric field in which the electric force on a proton is equal in magnitude to its weight?

Vishal Gupta
Vishal Gupta
Numerade Educator
02:38

Problem 28

The earth has a net electric charge that causes a field at points near its surface equal to 150 N$/$C and directed in toward the center of the earth. (a) What magnitude and sign of charge would a 60-kg human have to acquire to overcome his or her weight by the force exerted by the earth's electric field? (b) What would be the force of repulsion between two people each with the charge calculated in part (a) and separated by a distance of 100 m? Is use of the earth's electric field a feasible means of flight? Why or why not?

Ze-Han Lee
Ze-Han Lee
Numerade Educator
14:54

Problem 29

An electron is projected with an initial speed $v_0 =$ 1.60 $\times$ $10^6$ m$/$s into the uniform field between two parallel plates ($\textbf{Fig. E21.29}$). Assume that the field between the plates is uniform and directed vertically downward and that the field outside the plates is zero. The electron enters the field at a point midway between the plates. (a) If the electron just misses the upper plate as it emerges from the field, find the magnitude of the electric field. (b) Suppose that the electron in Fig. E21.29 is replaced by a proton with the same initial speed $v_0$ . Would the proton hit one of the plates? If not, what would be the magnitude and direction of its vertical displacement as it exits the region between the plates? (c) Compare the paths traveled by the electron and the proton, and explain the differences. (d) Discuss whether it is reasonable to ignore the effects of gravity for each particle.

Jayashree Behera
Jayashree Behera
Numerade Educator
02:54

Problem 30

(a) Calculate the magnitude and direction (relative to the $+ x$-axis) of the electric field in Example 21.6. (b) A $-$2.5-nC point charge is placed at point $P$ in Fig. 21.19. Find the magnitude and direction of (i) the force that the $-$8.0-nC charge at the origin exerts on this charge and (ii) the force that this charge exerts on the $-$8.0-nC charge at the origin.

Ze-Han Lee
Ze-Han Lee
Numerade Educator
05:46

Problem 31

In Exercise 21.29, what is the speed of the electron as it emerges from the field?

Jayashree Behera
Jayashree Behera
Numerade Educator
02:32

Problem 32

A uniform electric field exists in the region between two oppositely charged plane parallel plates. A proton is released from rest at the surface of the positively charged plate and strikes the surface of the opposite plate, 1.60 cm distant from the first, in a time interval of 3.20 $\times \space 10^{-6}$ s. (a) Find the magnitude of the electric field. (b) Find the speed of the proton when it strikes the negatively charged plate.

Ze-Han Lee
Ze-Han Lee
Numerade Educator
03:43

Problem 33

A point charge is at the origin. With this point charge as the source point, what is the unit vector $\hat{r}$ in the direction of the field point (a) at $x = 0, \space y = -$1.35 m; (b) at $x =$ 12.0 cm, $y =$ 12.0 cm; (c) at $x = -$1.10 m, $y =$ 2.60 m ? Express your results in terms of the unit vectors $\hat{\imath}$ and $\hat{\jmath}$.

Jayashree Behera
Jayashree Behera
Numerade Educator
02:20

Problem 34

A $+$8.75-$\mu$C point charge is glued down on a horizontal frictionless table. It is tied to a -6.50-$\mu$C point charge by a light, nonconducting 2.50-cm wire. A uniform electric field of magnitude 1.85 $\times 10^8$ N$/$C is directed parallel to the wire, as shown in $\textbf{Fig. E21.34.}$ (a) Find the tension in the wire. (b) What would the tension be if both charges were negative?

Narayan Hari
Narayan Hari
Numerade Educator
10:14

Problem 35

(a) An electron is moving east in a uniform electric field of 1.50 N$/$C directed to the west. At point $A$, the velocity of the electron is 4.50 $\times 10^5$ m$/$s toward the east. What is the speed of the electron when it reaches point B, 0.375 m east of point A? (b) A proton is moving in the uniform electric field of part (a). At point $A$, the velocity of the proton is 1.90 $\times 10^4$ m$/$s, east. What is the speed of the proton at point $B$?

Jayashree Behera
Jayashree Behera
Numerade Educator
02:13

Problem 36

Two point charges $Q$ and $+$q (where q is positive) produce the net electric field shown at point $P$ in $\textbf{Fig. E21.36.}$ The field points parallel to the line connecting the two charges. (a) What can you conclude about the sign and magnitude of $Q$? Explain your reasoning. (b) If the lower charge were negative instead, would it be possible for the field to have the direction shown in the figure? Explain your reasoning.

Ze-Han Lee
Ze-Han Lee
Numerade Educator
09:26

Problem 37

Two positive point charges $q$ are placed on the $x$-axis, one at $x = a$ and one at $x = -a$. (a) Find the magnitude and direction of the electric field at $x = 0$. (b) Derive an expression for the electric field at points on the x-axis. Use your result to graph the $x$-component of the electric field as a function of $x$, for values of $x$ between $-$4a and $+$4a.

Jayashree Behera
Jayashree Behera
Numerade Educator
03:34

Problem 38

The two charges $q_1$ and $q_2$ shown in $\textbf{Fig. E21.38}$ have equal magnitudes. What is the direction of the net electric field due to these two charges at points $A$ (midway between the charges), $B$, and $C$ if (a) both charges are negative, (b) both charges are positive, (c) $q_1$ is positive and $q_2$ is negative.

Ze-Han Lee
Ze-Han Lee
Numerade Educator
16:24

Problem 39

A $+$2.00-nC point charge is at the origin, and a second $-$5.00-nC point charge is on the $x$-axis at $x = $0.800 m. (a) Find the electric field (magnitude and direction) at each of the following points on the x-axis: (i) $x =$ 0.200 m; (ii) $x =$ 1.20 m; (iii) $x = -$0.200 m. (b) Find the net electric force that the two charges would exert on an electron placed at each point in part (a).

Vidhi Bhatt
Vidhi Bhatt
Numerade Educator
04:20

Problem 40

Repeat Exercise 21.39, but now let the charge at the origin be $-4.00 nC$.

Ze-Han Lee
Ze-Han Lee
Numerade Educator
06:02

Problem 41

Three negative point charges lie along a line as shown in $\textbf{Fig. E21.41.}$ Find the magnitude and direction of the electric field this combination of charges produces at point $P$, which lies 6.00 cm from the $-$2.00-$\mu$C charge measured perpendicular to the line connecting the three charges.

Sheh Lit Chang
Sheh Lit Chang
University of Washington
02:53

Problem 42

A point charge is placed at each corner of a square with side length $a$. All charges have magnitude $q$. Two of the charges are positive and two are negative ($\textbf{Fig. E21.42}$). What is the direction of the net electric field at the center of the square due to the four charges, and what is its magnitude in terms of $q$ and $a$?

Ze-Han Lee
Ze-Han Lee
Numerade Educator
12:41

Problem 43

Two point charges are separated by 25.0 cm ($\textbf{Fig. E21.43}$). Find the net electric field these charges produce at (a) point $A$ and (b) point $B$. (c) What would be the magnitude and direction of theelectric force this combination of charges would produce on a proton at $A$?

NG
Nathan Grieser
University of Oklahoma
03:27

Problem 44

Point charge $q_1 = -$5.00 nC is at the origin and point charge $q_2 = +$3.00 nC is on the $x$-axis at $x = $3.00 cm. Point $P$ is on the $y$-axis at $y = $4.00 cm. (a) Calculate the electric fields $\overrightarrow{E_1}$ and $\overrightarrow{E_2}$ at point $P$ due to the charges $q_1$ and $q_2$ . Express your results in terms of unit vectors (see Example 21.6). (b) Use the results of part (a) to obtain the resultant field at $P$, expressed in unit vector form.

Ze-Han Lee
Ze-Han Lee
Numerade Educator
13:03

Problem 45

If two electrons are each 1.50 $\times \space 10^{-10}$ m from a proton ($\textbf{Fig. E21.45}$), find the magnitude and direction of the net electric force they will exert on the proton.

Jayashree Behera
Jayashree Behera
Numerade Educator
03:09

Problem 46

A nerve signal is transmitted through a neuron when an excess of $Na^+$ ions suddenly enters the axon, a long cylindrical part of the neuron. Axons are approximately 10.0 $\mu$m in diameter, and measurements show that about 5.6 $\times \space 10^{11} \space Na^+$ions per meter (each of charge $+e$) enter during this process. Although the axon is a long cylinder, the charge does not all enter everywhere at the same time. A plausible model would be a series of point charges moving along the axon. Consider a 0.10-mm length of the axon and model it as a point charge. (a) If the charge that enters each meter of the axon gets distributed uniformly along it, how many coulombs of charge enter a 0.10-mm length of the axon? (b) What electric field (magnitude and direction) does the sudden influx of charge produce at the surface of the body if the axon is 5.00 cm below the skin? (c) Certain sharks can respond to electric fields as weak as 1.0 $\mu N/C$. How far from this segment of axon could a shark be and still detect its electric field?

Salamat Ali
Salamat Ali
Numerade Educator
29:37

Problem 47

In a rectangular coordinate system a positive point charge $q = 6.00 \times \space 10^{-9} C$ is placed at the point $x = +0.150 m, y = 0,$ and an identical point charge is placed at $x = -0.150 m, y = 0.$ Find the $x$- and $y$-components, the magnitude, and the direction of the electric field at the following points: (a) the origin; (b) $x =$ 0.300 m, $y =$ 0; (c) $x =$ 0.150 m, $y = -$0.400 m; (d) $x = 0, $y =$ 0.200 m.

Stanley Enemuo
Stanley Enemuo
Numerade Educator
View

Problem 48

A point charge $q_1 = -$4.00 nC is at the point $x =$ 0.600 m, $y =$ 0.800 m, and a second point charge $q_2 = +$6.00 nC is at the point $x =$ 0.600 m, $y =$ 0. Calculate the magnitude and direction of the net electric field at the origin due to these two point charges.

VM
Venuja Marasinghe
Numerade Educator
09:47

Problem 49

A charge of $-$6.50 nC is spread uniformly over the surface of one face of a nonconducting disk of radius 1.25 cm. (a) Find the magnitude and direction of the electric field this disk produces at a point $P$ on the axis of the disk a distance of 2.00 cm from its center. (b) Suppose that the charge were all pushed away from the center and distributed uniformly on the outer rim of the disk. Find the magnitude and direction of the electric field at point $P.$ (c) If the charge is all brought to the center of the disk, find the magnitude and direction of the electric field at point $P.$ (d) Why is the field in part (a) stronger than the field in part (b)? Why is the field in part (c) the strongest of the three fields?

Jayashree Behera
Jayashree Behera
Numerade Educator
01:27

Problem 50

A very long, straight wire has charge per unit length $3.20 \times 10^{-10}$ C/m. At what distance from the wire is the electric-field magnitude equal to 2.50 N$/$C?

Ze-Han Lee
Ze-Han Lee
Numerade Educator
02:14

Problem 51

A ring-shaped conductor with radius $a =$ 2.50 cm has
a total positive charge $Q = +$0.125 nC uniformly distributed
around it (see Fig. 21.23). The center of the ring is at the origin of
coordinates $O$. (a) What is the electric field (magnitude and direction)
at point $P$, which is on the $x$-axis at $x =$ 40.0 cm? (b) A point
charge $q = -2.50 \space \mu$C is placed at $P$. What are the magnitude and
direction of the force exerted by the charge $q$ $on$ the ring?

Jayashree Behera
Jayashree Behera
Numerade Educator
03:06

Problem 52

A straight, nonconducting plastic wire 8.50 cm long
carries a charge density of $+$175 nC$/$m distributed uniformly
along its length. It is lying on a horizontal tabletop. (a) Find the
magnitude and direction of the electric field this wire produces
at a point 6.00 cm directly above its midpoint. (b) If the wire is
now bent into a circle lying flat on the table, find the magnitude
and direction of the electric field it produces at a point 6.00 cm
directly above its center.

Ze-Han Lee
Ze-Han Lee
Numerade Educator
05:54

Problem 53

Point charges $q_1 = -$4.5 nC and $q_2 = +$4.5 nC are
separated by 3.1 mm, forming an electric dipole. (a) Find the
electric dipole moment (magnitude and direction). (b) The charges
are in a uniform electric field whose direction makes an angle
of 36.9$^\circ$ with the line connecting the charges. What is the magnitude
of this field if the torque exerted on the dipole has magnitude
$7.2 \times 10^{-9}$ N $\cdot$ m ?

Jayashree Behera
Jayashree Behera
Numerade Educator
01:45

Problem 54

The ammonia molecule (NH$_3$) has a dipole moment of $5.0 \times 10^{30}$ C $\cdot$ m. Ammonia molecules in the gas phase are placed in a uniform electric field $\overrightarrow{E}$ with magnitude $1.6 \times 10^6$ N$/$C. (a) What is the change in electric potential energy when the dipole moment of a molecule changes its orientation with respect to $\overrightarrow{E}$ from parallel to perpendicular? (b) At what absolute temperature $T$ is the average translational kinetic energy $\frac{3}{2} kT$ of a molecule equal to the change in potential energy calculated in part (a)? (Note: Above this temperature, thermal agitation prevents the dipoles from aligning with the electric field.)

Salamat Ali
Salamat Ali
Numerade Educator
05:08

Problem 55

An electric dipole with dipole moment $\overrightarrow{p}$ is in a uniform external electric field $\overrightarrow{E}$ . (a) Find the orientations of the dipole for which the torque on the dipole is zero. (b) Which of the orientations in part (a) is stable, and which is unstable? ($Hint:$ Consider a small rotation away from the equilibrium position and see what happens.) (c) Show that for the stable orientation in part (b), the dipole's own electric field tends to oppose the external field.

Jayashree Behera
Jayashree Behera
Numerade Educator
02:32

Problem 56

The dipole moment of the water molecule ($H_2O$) is 6.17 $\times$ $10^{-30}$ C $\cdot$ m. Consider a water molecule located at the origin whose dipole moment $\overrightarrow{p}$ points in the $+x$-direction. A chlorine ion (C1$^-$), of charge $-1.60 \times 10^{-19}$ C, is located at $x =$ 3.00 $\times 10^{-9}$ m. Find the magnitude and direction of the electric force that the water molecule exerts on the chlorine ion. Is this force attractive or repulsive? Assume that $x$ is much larger than the separation $d$ between the charges in the dipole, so that the approximate expression for the electric field along the dipole axis derived in Example 21.14 can be used.

Salamat Ali
Salamat Ali
Numerade Educator
09:12

Problem 57

Three charges are at the corners of an isosceles triangle as shown in $\textbf{Fig. E21.57.}$ The $\pm$5.00-$\mu$C charges form a dipole. (a) Find the force (magnitude and direction) the $-$10.00$\mu$C charge exerts on the dipole. (b) For an axis perpendicular to the line connecting the $\pm$5.00-$\mu$C charges at the midpoint of this line, find the torque (magnitude and direction) exerted on the dipole by the $-10.00 \space \mu$C charge.

Sheh Lit Chang
Sheh Lit Chang
University of Washington
04:21

Problem 58

Consider the electric dipole of Example 21.14. (a) Derive an expression for the magnitude of the electric field produced by the dipole at a point on the $x-axis$ in Fig. 21.33. What is the direction of this electric field? (b) How does the electric field at points on the $x-axis$ depend on $x$ when $x$ is very large?

Sourav Kumar
Sourav Kumar
Numerade Educator
07:04

Problem 59

Four identical charges $Q$ are placed at the corners of
a square of side $L$. (a) In a free-body diagram, show all of the
forces that act on one of the charges. (b) Find the magnitude and
direction of the total force exerted on one charge by the other
three charges.

Jayashree Behera
Jayashree Behera
Numerade Educator
05:35

Problem 60

Two charges are placed on the $x$-axis: one, of 2.50 $\mu C$, at the origin and the other, of $-3.50 \mu C$, at x = 0.600 m $\textbf{(Fig. P21.60).}$ Find the position on the $x$-axis where the net force
on a small charge $+q$ would be zero.

Vishal Gupta
Vishal Gupta
Numerade Educator
05:11

Problem 61

A charge $q_1 = +$5.00 nC is placed at the origin of an $xy$-coordinate system, and a charge $q_2 = -$2.00 nC is placed on the positive $x$-axis at $x = $4.00 cm. (a) If a third charge $q_3 = +$6.00 nC is now placed at the point $x =$ 4.00 cm, $y =$ 3.00 cm, find the $x$- and $y$-components of the total force exerted on this charge by the other two. (b) Find the magnitude and direction of
this force.

Salamat Ali
Salamat Ali
Numerade Educator
04:18

Problem 62

Two identical spheres with mass m are hung from silk threads of length L $\textbf{(Fig. P21.62).}$ The spheres have the same charge, so $q_1 = q_2 = q$. The radius of each sphere is very small compared to the distance between the spheres, so they may be treated as point charges. Show that if the angle $\theta$ is small, the equilibrium separation $d$ between the spheres is $d = (q^2L/2\pi\epsilon_0 mg)^{1/3}$. ($Hint$: If $\theta$ is small, then tan $\theta \cong sin \theta$.)

Ze-Han Lee
Ze-Han Lee
Numerade Educator
04:55

Problem 63

Two small spheres with mass $m =$ 15.0 g are hung by silk threads of length $L =$ 1.20 m from a common point (Fig. P21.62). When the spheres are given equal quantities of negative charge, so that $q_1 = q_2 = q$, each thread hangs at $\theta = 25.0^\circ$ from the vertical. (a) Draw a diagram showing the forces on each sphere. Treat the spheres as point charges. (b) Find the magnitude of $q$. (c) Both threads are now shortened to length $L =$ 0.600 m, while the charges $q_1$ and $q_2$ remain unchanged. What new angle will each thread make with the vertical? ($Hint$: This part of the problem can be solved numerically by using trial values for $\theta$ and adjusting the values of $\theta$ until a self-consistent answer is obtained.)

Narayan Hari
Narayan Hari
Numerade Educator
07:31

Problem 64

Two identical spheres are each attached to silk threads of length $L =$ 0.500 m and hung from a common point (Fig. P21.62). Each sphere has mass $m =$ 8.00 g. The radius of each sphere is very small compared to the distance between the spheres, so they may be treated as point charges. One sphere is given positive charge $q_1$ , and the other a different positive charge $q_2$ ; this causes the spheres to separate so that when the spheres are in equilibrium, each thread makes an angle $\theta = 20.0^\circ$ with the vertical. (a) Draw a free-body diagram for each sphere when in equilibrium, and label all the forces that act on each sphere. (b) Determine the magnitude of the electrostatic force that acts on each sphere, and determine the tension in each thread. (c) Based on the given information, what can you say about the magnitudes of $q_1$ and $q_2$? Explain. (d) A small wire is now connected between the spheres, allowing charge to be transferred from one sphere to the other until the two spheres have equal charges; the wire is then removed. Each thread now makes an angle of 30.0$^\circ$ with the vertical. Determine the original charges. ($Hint$: The total charge on the pair of spheres is conserved.)

Ze-Han Lee
Ze-Han Lee
Numerade Educator
06:07

Problem 65

A small 12.3-g plastic ball is tied to a very light 28.6-cm string that is attached to the vertical wall of a room ($\textbf{Fig. P21.65}$). A uniform horizontal electric field exists in this room. When the ball has been given an excess charge of $-1.11 \space \mu$C, you observe that it remains suspended, with the string making an angle of 17.4$^\circ$ with the wall. Find the magnitude and direction of the electric field in the room.

Jayashree Behera
Jayashree Behera
Numerade Educator
04:01

Problem 66

Point charge $q_1 = -6.00 \times \space 10^{-6}$ C is on the $x$-axis at $x = -0.200\space \mathrm{m}$. Point charge $q_2$ is on the $x$-axis at $x = +0.400 \space \mathrm{m}$. Point charge $q_3 = +3.00 \times \space 10^{-6}$ C is at the origin. What is $q_2$ (magnitude and sign) (a) if the net force on $q_3$ is $6.00 \mathrm{N}$ in the $+x-\mathrm{direction}$; (b) if the net force on $q_3$ is $6.00 \mathrm{N}$ in the $-x-\mathrm{direction}$?

Ze-Han Lee
Ze-Han Lee
Numerade Educator
05:48

Problem 67

Two particles having charges $q_1 =$ 0.500 nC and $q_2 =$ 8.00 nC are separated by a distance of 1.20 m. At what point along the line connecting the two charges is the total electric field due to the two charges equal to zero?

Jayashree Behera
Jayashree Behera
Numerade Educator
02:18

Problem 68

A $-$3.00-nC point charge is on the $x$-axis at $x =$ 1.20 m. A second point charge, $Q,$ is on the $x$-axis at -0.600 m. What must be the sign and magnitude of $Q$ for the resultant electric field at the origin to be (a) 45.0 N$/$C in the $+$x-direction, (b) 45.0 N$/$C in the $-$x-direction?

Ze-Han Lee
Ze-Han Lee
Numerade Educator
09:32

Problem 69

A charge $+Q$ is located at the origin, and a charge $+Q$ is at distance $d$ away on the $x$-axis. Where should a third charge, $q$, be placed, and what should be its sign and magnitude, so that all three charges will be in equilibrium?

Jayashree Behera
Jayashree Behera
Numerade Educator
04:07

Problem 70

A charge of $-$3.00 nC is placed at the origin of an $xy$-coordinate system, and a charge of 2.00 nC is placed on the $y$-axis at $y =$ 4.00 cm. (a) If a third charge, of 5.00 nC, is now placed at the point $x =$ 3.00 cm, $y =$ 4.00 cm, find the $x$- and $y$-components of the total force exerted on this charge by the other two charges. (b) Find the magnitude and direction of this force.

Ze-Han Lee
Ze-Han Lee
Numerade Educator
15:04

Problem 71

Three identical point charges $q$ are placed at each of three corners of a square of side $L$. Find the magnitude and direction of the net force on a point charge $-3q$ placed (a) at the center of the square and (b) at the vacant corner of the square. In each case, draw a free-body diagram showing the forces exerted on the $-3q$ charge by each of the other three charges.

Jayashree Behera
Jayashree Behera
Numerade Educator
04:17

Problem 72

Two point charges $q_1$ and $q_2$ are held in place $4.50 cm$ apart. Another point charge $Q = -1.75 \space \mu C$, of mass 5.00 g, is initially located $3.00 cm$ from both of these charges ($\textbf{Fig. P21.72}$) and released from rest. You observe that the initial acceleration of $Q$ is 324 m$/$s$^2$ upward, parallel to the line connecting the two point charges. Find $q_1$ and $q_2$.

Ze-Han Lee
Ze-Han Lee
Numerade Educator
09:17

Problem 73

Imagine two 1.0-g bags of protons, one at the earth's north pole and the other at the south pole. (a) How many protons are in each bag? (b) Calculate the gravitational attraction and the electric repulsion that each bag exerts on the other. (c) Are the forces in part (b) large enough for you to feel if you were holding one of the bags?

Jayashree Behera
Jayashree Behera
Numerade Educator
04:14

Problem 74

Two tiny spheres of mass 6.80 mg carry charges of equal magnitude, 72.0 nC, but opposite sign. They are tied to the same ceiling hook by light strings of length 0.530 m. When a horizontal uniform electric field $E$ that is directed to the left is turned on, the spheres hang at rest with the angle $\theta$ between the strings equal to 58.0$^\circ \space (\textbf{Fig.P21.74}$). (a) Which ball (the one on the right or the one on the left) has positive charge? (b) What is the magnitude $E$ of the field?

Supratim Pal
Supratim Pal
Numerade Educator
03:33

Problem 75

Consider a model of a hydrogen atom in which an electron is in a circular orbit of radius $r = 5.29 \times \space 10^{-11}$ m around a stationary proton. What is the speed of the electron in its orbit?

Jayashree Behera
Jayashree Behera
Numerade Educator
02:38

Problem 76

The earth has a downward-directed electric field near its surface of about 150 N$/$C. If a raindrop with a diameter of 0.020 mm is suspended, motionless, in this field, how many excess electrons must it have on its surface?

Ze-Han Lee
Ze-Han Lee
Numerade Educator
09:22

Problem 77

A proton is projected into a uniform electric field that points vertically upward and has magnitude $E$. The initial velocity of the proton has a magnitude $v_0$ and is directed at an angle $\alpha$ below the horizontal. (a) Find the maximum distance $h_{max}$ that the proton descends vertically below its initial elevation. Ignore gravitational forces. (b) After what horizontal distance d does the proton return to its original elevation? (c) Sketch the trajectory of the proton. (d) Find the numerical values of $h_{max}$ and $d$ if $E =$ 500 N$/$C, $v_0 =$ 4.00 $\times 10^5$ m$/$s, and $\alpha =$ 30.0$^\circ$.

Ryan Williams
Ryan Williams
Numerade Educator
07:15

Problem 78

A small object with mass $m$, charge $q$, and initial speed $v_0 = 5.00 \times 10^3$ m$/$s is projected into a uniform electric field between two parallel metal plates of length 26.0 cm ($\textbf{Fig. P21.78}$). The electric field between the plates is directed downward and has magnitude $E =$ 800 N$/$C. Assume that the field is zero outside the region between the plates. The separation between the plates is large enough for the object to pass between the plates without hitting the lower plate. After passing through the field region, the object is deflected downward a vertical distance $d =$ 1.25 cm from its original direction of motion and reaches a collecting plate that is $56.0 \space cm$ from the edge of the parallel plates. Ignore gravity and air resistance. Calculate the object's charge-to-mass ratio, $q/m$.

Supratim Pal
Supratim Pal
Numerade Educator
16:50

Problem 79

Positive charge $Q$ is distributed uniformly along the $x$-axis from $x = 0$ to $x =$ a. A positive point charge $q$ is located on the positive $x$-axis at $x = a + \space r$, a distance $r$ to the right of the end of $Q \space (\textbf{Fig. P21.79}$). (a) Calculate the $x$- and $y$-components of the electric field produced by the charge distribution $Q$ at points on the positive $x$-axis where $x \space >$ a. (b) Calculate the force (magnitude and direction) that the charge distribution $Q$ exerts on $q$. (c) Show that if $r \space \gg a$, the magnitude of the force in part (b) is approximately $Qq/4\pi\epsilon_0 r^2$. Explain why this result is obtained.

Jayashree Behera
Jayashree Behera
Numerade Educator
04:38

Problem 80

In a region where there is a uniform electric field that is upward and has magnitude 3.60 $\times 10^4 \space N/$C, a small object is projected upward with an initial speed of 1.92 m$/$s. The object travels upward a distance of 6.98 cm in 0.200 s. What is the object's charge-to-mass ratio $q/m$? Assume $g = 9.80 \space m/s^2$, and ignore air resistance.

Ze-Han Lee
Ze-Han Lee
Numerade Educator
12:16

Problem 81

A negative point charge $q_1 = -4.00$ nC is on the $x$-axis at $x =$ 0.60 m. A second point charge $q_2$ is on the $x$-axis at $x = -$1.20 m. What must the sign and magnitude of $q_2$ be for the net electric field at the origin to be (a) 50.0 N$/$C in the $+x$-direction and (b) 50.0 N$/$C in the $-$x-direction?

Jayashree Behera
Jayashree Behera
Numerade Educator
10:32

Problem 82

Positive charge $Q$ is distributed uniformly along the positive $y$-axis between $y = 0$ and $y = a$. A negative point charge $-q$ lies on the positive $x$-axis, a distance $x$ from the origin ($\textbf{Fig. P21.82}$). (a) Calculate the $x$- and $y$-components of the electric field produced by the charge distribution $Q$ at points on the positive $x$-axis. (b) Calculate the $x$- and $y$-components of the force that the charge distribution $Q$ exerts on $q$. (c) Show that if $x \gg$ a, $F_x \cong -$$Qq4\pi\epsilon_0 x^2$ and $F_y \cong \space +Qqa/8\pi\epsilon_0 x^3$. Explain why this result is obtained.

Ze-Han Lee
Ze-Han Lee
Numerade Educator
16:56

Problem 83

A uniformly charged disk like the disk in Fig. 21.25 has radius 2.50 cm and carries a total charge of 7.0 $\times 10^{-12}$ C. (a) Find the electric field (magnitude and direction) on the $x$-axis at $x =$ 20.0 cm. (b) Show that for $x \gg R, Eq$. (21.11) becomes $E = Q/4\pi\epsilon_0 x^2$, where $Q$ is the total charge on the disk. (c) Is the magnitude of the electric field you calculated in part (a) larger or smaller than the electric field 20.0 cm from a point charge that has the same total charge as this disk? In terms of the approximation used in part (b) to derive $E = Q/4\pi\epsilon_0 x^2$ for a point charge from Eq. (21.11), explain why this is so. (d) What is the percent difference between the electric fields produced by the finite disk and by a point charge with the same charge at $x =$ 20.0 cm and at $x =$ 10.0 cm?

Linda Winkler
Linda Winkler
Numerade Educator
02:48

Problem 84

A small sphere with mass $m$ carries a positive charge $q$ and is attached to one end of a silk fiber of length $L$. The other end of the fiber is attached to a large vertical insulating sheet that has a positive surface charge density $\sigma$. Show that when the sphere is in equilibrium, the fiber makes an angle equal to arctan ($q\sigma/2mg\epsilon_0$) with the vertical sheet.

Ze-Han Lee
Ze-Han Lee
Numerade Educator
06:01

Problem 85

Negative charge $-Q$ is distributed uniformly around a quarter-circle of radius a that lies in the first quadrant, with the center of curvature at the origin. Find the $x$- and $y$-components of the net electric field at the origin.

Narayan Hari
Narayan Hari
Numerade Educator
20:52

Problem 86

A semicircle of radius a is in the first and second quadrants, with the center of curvature at the origin. Positive charge $+Q$ is distributed uniformly around the left half of the semicircle, and negative charge $-Q$ is distributed uniformly around the right half of the semicircle ($\textbf{Fig.P21.86}$).What are the magnitude and direction of the net electric field at the origin produced by this distribution of charge?

Kebur Fantahun
Kebur Fantahun
Numerade Educator
06:04

Problem 87

Two 1.20-m nonconducting rods meet at a right angle. One rod carries $+$2.50 $\mu$C of charge distributed uniformly along its length, and the other carries $-$2.50 $\mu$C distributed uniformly along it ($\textbf{Fig. P21.87}$). (a) Find the magnitude and direction of the electric field these rods produce at point $P$, which is 60.0 cm from each rod. (b) If an electron is released at $P$, what are the magnitude and direction of the net force that these rods exert on it?

Sheh Lit Chang
Sheh Lit Chang
University of Washington
02:59

Problem 88

Two very large parallel sheets are 5.00 cm apart. Sheet $A$ carries a uniform surface charge density of $-8.80 \space \mu$C$/m^2$, and sheet $B$, which is to the right of $A$, carries a uniform charge density of $-11.6 \space \mu$C$/m^2$. Assume that the sheets are large enough to be treated as infinite. Find the magnitude and direction of the net electric field these sheets produce at a point (a) 4.00 cm to the right of sheet $A$; (b) 4.00 cm to the left of sheet $A$; (c) 4.00 cm to the right of sheet $B$.

Ze-Han Lee
Ze-Han Lee
Numerade Educator
04:24

Problem 89

Repeat Problem 21.88 for the case where sheet $B$ is positive.

Salamat Ali
Salamat Ali
Numerade Educator
03:22

Problem 90

Two very large horizontal sheets are 4.25 cm apart and
carry equal but opposite uniform surface charge densities of
magnitude $\sigma$. You want to use these sheets to hold stationary in
the region between them an oil droplet of mass 486 $\mu$g that carries
an excess of five electrons. Assuming that the drop is in vacuum,
(a) which way should the electric field between the plates point,
and (b) what should $\sigma$ be?

Ze-Han Lee
Ze-Han Lee
Numerade Educator
21:55

Problem 91

A thin disk with a circular hole at its center, called an $annulus$, has inner radius $R_1$ and outer radius $R_2 \space (\textbf{Fig. P21.91}$). The disk has a uniform positive surface charge density $\sigma$ on its surface. (a) Determine the total electric charge on the annulus. (b) The annulus lies in the $yz$-plane, with its center at the origin. For an arbitrary point on the $x$-axis (the axis of the annulus), find the magnitude and direction of the electric field $\overrightarrow{E}$. Consider points both above and below the annulus. (c) Show that at points on the $x$-axis that are sufficiently close to the origin, the magnitude of the electric field is approximately proportional to the distance between the center of the annulus and the point. How close is "sufficiently close"? (d) A point particle with mass $m$ and negative charge $-q$ is free to move along the $x$-$axis$ (but cannot move off the axis). The particle is originally placed at rest at $x = 0.01 \space R_1$ and released. Find the frequency of oscillation of the particle. ($Hint$: Review Section 14.2. The annulus is held stationary.)

Linda Winkler
Linda Winkler
Numerade Educator
04:25

Problem 92

Inkjet printers can be described as either continuous or drop-on-demand. In a continuous inkjet printer, letters are built up by squirting drops of ink at the paper from a rapidly moving nozzle. You are part of an engineering group working on the design of such a printer. Each ink drop will have a mass of 1.4 $\times \space 10^{-8}$ g. The drops will leave the nozzle and travel toward the paper at 50 m$/$s, passing through a charging unit that gives each drop a positive charge $q$ by removing some electrons from it. The drops will then pass between parallel deflecting plates, 2.0 cm long, where there is a uniform vertical electric field with magnitude 8.0 $\times \space 10^4 \space N/C$. Your team is working on the design of the charging unit that places the charge on the drops. (a) If a drop is to be deflected 0.30 mm by the time it reaches the end of the deflection plates, what magnitude of charge must be given to the drop? How many electrons must be removed from the drop to give it this charge? (b) If the unit that produces the stream of drops is redesigned so that it produces drops with a speed of 25 $m/s$, what $q$ value is needed to achieve the same 0.30-mm deflection?

Salamat Ali
Salamat Ali
Numerade Educator
06:10

Problem 93

Two small spheres, each carrying a net positive charge, are separated by $0.400 m$. You have been asked to perform measurements that will allow you to determine the charge on each sphere. You set up a coordinate system with one sphere ($charge \space q_1$) at the origin and the other sphere ($charge \space q_2$) at $x = +$0.400 m. Available to you are a third sphere with net charge $q_3 = 4.00 \times 10^{-6}$ C and an apparatus that can accurately measure the location of this sphere and the net force on it. First you place the third sphere on the $x$-axis at $x =$ 0.200 m; you measure the net force on it to be 4.50 N in the $+ x$-direction. Then you move the third sphere to $x = +$0.600 m and measure the net force on it now to be 3.50 N in the $+ x$-direction. (a) Calculate $q_1$ and $q_2$. (b) What is the net force (magnitude and direction) on $q_3$ if it is placed on the $x$-axis at $x = -$0.200 m? (c) At what value of $x$ (other than $x = \pm \infty$) could $q_3$ be placed so that the net force on it is zero?

Salamat Ali
Salamat Ali
Numerade Educator
04:04

Problem 94

Positive charge $Q$ is distributed uniformly around a very thin conducting ring of radius $a$, as in Fig. 21.23. You measure the electric field $E$ at points on the ring axis, at a distance $x$ from the center of the ring, over a wide range of values of $x$. (a) Your results for the larger values of $x$ are plotted in Fig. P21.94a as $Ex^2$ versus $x$. Explain why the quantity $Ex^2$ approaches a constant value as $x$ increases. Use Fig. P21.94a to calculate the net charge $Q$ on the ring. (b) Your results for smaller values of $x$ are plotted in Fig. P21.94b as $E/x$ versus $x$. Explain why $E/x$ approaches a constant value as $x$ approaches zero. Use Fig. P21.94b to calculate $a$.

Suzanne W.
Suzanne W.
Numerade Educator
08:11

Problem 95

Three charges are placed as shown in $\textbf{Fig. P21.95}$. The magnitude of $q_1$ is 2.00 $\mu$C, but its sign and the value of the charge $q_2$ are not known. Charge $q_3$ is $+$4.00 $\mu$C, and the net force $\overrightarrow{F}$ on $q_3$ is entirely in the negative $x$-direction. (a) Considering the different possible signs of $q_1$, there are four possible force diagrams representing the forces $\overrightarrow{F}_1$ and $\overrightarrow{F}_2$ that $q_1$ and $q_2$ exert on $q_3$ . Sketch these four possible force configurations. (b) Using the sketches from part (a) and the direction of $\overrightarrow{F}$ , deduce the signs of the charges $q_1$ and $q_2$ . (c) Calculate the magnitude of $q_2$ . (d) Determine $F$, the magnitude of the net force on $q_3$ .

Ajay Singhal
Ajay Singhal
Numerade Educator
05:30

Problem 96

Two charges are placed as shown in $\textbf{Fig. P21.96}$. The magnitude of $q_1$ is 3.00 $\mu$C, but its sign and the value of the charge $q_2$ are not known. The direction of the net electric field $\overrightarrow{E}$ at point $P$ is entirely in the negative $y$-direction. (a) Considering the different possible signs of $q_1$ and $q_2$ , four possible diagrams could represent the electric fields $\overrightarrow{E}_1$ and $\overrightarrow{E}_2$ produced by $q_1$ and $q_2$. Sketch the four possible electric-field configurations. (b) Using the sketches from part (a) and the direction of $\overrightarrow{E}$ , deduce the signs of $q_1$ and $q_2$ . (c) Determine the magnitude of $\overrightarrow{E}$.

Ze-Han Lee
Ze-Han Lee
Numerade Educator
14:48

Problem 97

Two thin rods of length $L$ lie along the $x$-axis, one between $x = \frac{1}{2} a$ and $x = \frac{1}{2} a + L$ and the other between $x = -\frac{1}{2} a$ and $x = -\frac{1}{2} a - L$. Each rod has positive charge $Q$ distributed uniformly along its length. (a) Calculate the electric field produced by the second rod at points along the positive x-axis. (b) Show that the magnitude of the force that one rod exerts on the other is

$$F = {Q^2 \over 4\pi\epsilon_0 L^2} ln [ {(a + L)^2 \over a(a + 2L)} ]$$

(c) Show that if $a$ $\gg$ $L$, the magnitude of this force reduces to $F = Q^2/4\pi\epsilon_0 a^2$. ($Hint$: Use the expansion ln $(1 + z) = z - \frac{1}{2} z^2 + \frac{1}{3} z^3 - \cdot\cdot\cdot$, valid for $\mid z \mid\ll1$. Carry $all$ expansions to at least order $L^2/a^2.$) Interpret this result.

Sheh Lit Chang
Sheh Lit Chang
University of Washington
00:55

Problem 98

Consider a bee with the mean electric charge found in the experiment. This charge represents roughly how many missing electrons? (a) $1.9 \times 10^8; (b) 3.0 \times 10^8; (c) 1.9 \times 10^{18}; (d) 3.0 \times 10^{18}.$

Ze-Han Lee
Ze-Han Lee
Numerade Educator
00:37

Problem 99

What is the best explanation for the observation that the electric charge on the stem became positive as the charged bee approached (before it landed)? (a) Because air is a good conductor, the positive charge on the bee's surface flowed through the air from bee to plant. (b) Because the earth is a reservoir of large amounts of charge, positive ions were drawn up the stem from the ground toward the charged bee. (c) The plant became electrically polarized as the charged bee approached. (d) Bees that had visited the plant earlier deposited a positive charge on the stem.

Jayashree Behera
Jayashree Behera
Numerade Educator
00:41

Problem 100

After one bee left a flower with a positive charge, that bee flew away and another bee with the same amount of positive charge flew close to the plant. Which diagram in $\textbf{Fig. P21.100}$ best represents the electric field lines between the bee and the flower?

Ze-Han Lee
Ze-Han Lee
Numerade Educator
01:39

Problem 101

In a follow-up experiment, a charge of $+40$ pC was placed at the center of an artificial flower at the end of a 30-cm long stem. Bees were observed to approach no closer than 15 cm from the center of this flower before they flew away. This observation suggests that the smallest external electric field to which bees may be sensitive is closest to which of these values? (a) $2.4 \space N/C; (b) 16 \space N/C; (c) 2.7 \times 10^{-10} \space N/C; (d) 4.8 \times 10^{-10} \space N/C.$

Jayashree Behera
Jayashree Behera
Numerade Educator