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Physics Mastery for Advanced High School Students: Complete Physics Review with 400 SAT and AP Physics Questions 2

Tony Rothman, Steve Warner

Chapter 9

Electricity and Magnetism Review - all with Video Answers

Educators

Chapter Questions

01:22

Problem 1

Two identical conducting spheres, $A$ and $B$ carry charges $+Q$ and $-Q$, respectively. A third, identical conducting sphere $C$ carries charge $Q=0$. Sphere $A$ is touched to sphere $C$ and separated. Next, sphere $B$ is touched to sphere $C$ and separated. Finally, $A$ is touched to $B$ and separated. What is the final charge on each sphere?
(A) $A=Q ; B=-Q ; C=0$
(B) $A=Q / 2 ; B=Q / 2 ; C=Q / 4$
(C) $A=Q / 8 ; B=Q / 8 ; C=-Q / 4$
(D) $A=Q / 2 ; B=-Q / 4 ; C=-Q / 4$
(E) $A=Q / 4 ; B=-Q / 8 ; C=-Q / 4$

Kayla Gephart
Kayla Gephart
Numerade Educator
01:31

Problem 2

Two conducting spheres of differing radii are in contact, as shown. A positively charged rod is touched to the large sphere and removed to a great distance. The large and small spheres are then separated. We can then say that
(A) the big sphere will be positively charged and the smaller sphere will be negatively charged.
(B) both spheres will be positively charged.
(C) the big sphere will be negatively charged and the smaller sphere will be positively charged.
(D) both spheres will be negatively charged.
(E) all the charge will migrate to the smaller sphere.

Dading Chen
Dading Chen
Numerade Educator
01:23

Problem 3

The positively charged rod is brought near the large sphere, but without touching it. The two spheres are separated and lastly the rod removed to a distance. We can then say that
(A) the big sphere will be positively charged and the smaller sphere will be negatively charged.
(B) both spheres will be positively charged.
(C) the big sphere will be negatively charged and the smaller sphere will be positively charged.
(D) both spheres will be negatively charged.
(E) all the charge will migrate to the smaller sphere.

RZ
Rubeena Zulfiqar
Numerade Educator
00:57

Problem 4

A negative charge $-Q$ is located at the position shown. At which of the labeled points is the electric field smallest?
(A) $\mathrm{A}$
(B) $\mathrm{B}$
(C) $\mathrm{C}$
(D) $\mathrm{D}$
(E) $\mathrm{E}$

Prem Bijarniya
Prem Bijarniya
Numerade Educator
01:30

Problem 5

At which pair of points is the field most nearly the same?
(A) B and C
(B) $\mathrm{B}$ and $\mathrm{A}$
(C) D and E
(D) $\mathrm{C}$ and $\mathrm{D}$
(E) A and D

Amrita Bhasin
Amrita Bhasin
Numerade Educator
00:21

Problem 6

At which point will a negative charge experience a force directly downward?
(A) $\mathrm{A}$
(B) $\mathrm{B}$
(C) $\mathrm{C}$
(D) $\mathrm{D}$
(E) $\mathrm{E}$

Stephen Zaffke
Stephen Zaffke
Numerade Educator
02:25

Problem 7

Two identical point charges $q_1$ and $q_2$ are at a distance $r$ apart. If the size of $q_1$ is doubled and the distance between them tripled, the strength of the electrical force between them
(A) goes up by a factor of 3 .
(B) goes down by a factor of 3 .
(C) goes down by a factor of 9 .
(D) goes down by a factor of $2 / 3$.
(E) goes down by a factor of $2 / 9$

Vysakh M
Vysakh M
Numerade Educator
04:21

Problem 8

The below fields represent electric or magnetic fields associated with a long current-carrying wire, a single positive charge, two oppositely charged particles, two positive charges, and the field between two oppositely charged parallel sheets.
(A) A, D, C, B, E
(B) E, A, D, C, B
(C) E, D, A, B, C
(D) D, E, C, B, A
(E) C, B, A, E, D

Dading Chen
Dading Chen
Numerade Educator
10:55

Problem 9

A positively charged plate sits above a negatively charged plate, as shown below.
An electron is shot off the top plate toward the bottom plate with nonzero initial velocity. The electron's maximum velocity is reached
(A) at the bottom plate.
(B) at the top plate.
(C) one-quarter of the distance between the plates.
(D) halfway between the plates.
(E) everywhere; the velocity is constant.

Vishal Gupta
Vishal Gupta
Numerade Educator
02:28

Problem 10

An electron is released from rest just above a very large, negatively charged sheet, which carries surface charge density $\sigma=5 \mathrm{nC} / \mathrm{m}^2$. When the electron is $0.5 \mathrm{~m}$ above the sheet its speed is most nearly
(A) $4 \times 10^8 \mathrm{~m} / \mathrm{s}$
(B) $3 \times 10^8 \mathrm{~m} / \mathrm{s}$
(C) $5 \times 10^7 \mathrm{~m} / \mathrm{s}$
(D) $1 \times 10^7 \mathrm{~m} / \mathrm{s}$
(E) $300 \mathrm{~m} / \mathrm{s}$

Zachary Warner
Zachary Warner
Numerade Educator
01:01

Problem 11

Suppose that the current $I$ in a solenoid is directly proportional to time: $I=b t$, where $b$ is a constant. Then the magnetic field inside the solenoid is best described by which graph of $B$ vs $t$ ?
(A) A
(B) $\mathrm{B}$
(C) $\mathrm{C}$
(D) D
(E) $\mathrm{E}$

Raj Bala
Raj Bala
Numerade Educator
01:32

Problem 12

A horseshoe magnet with a field of $0.15 \mathrm{~T}$ is moving at a constant velocity $\mathbf{v}=2.5 \mathrm{~m} / \mathrm{s}$ to the right and encounters a charge $q=-5 \mathrm{nC}$, as shown below.
The direction and magnitude the magnet exerts on the charge is:
(A) $1.875 \times 10^{-9} \mathrm{~N}$, to the right
(B) $1.875 \times 10^{-9} \mathrm{~N}$, into the page
(C) $1.875 \times 10^{-9} \mathrm{~N}$, out of the page
(D) $0.375 \times 10^{-9} \mathrm{~N}$, out of the page
(E) $0.375 \times 10^{-9} \mathrm{~N}$, into the page

Ajay Singhal
Ajay Singhal
Numerade Educator
05:53

Problem 13

A permanent bar magnet is at rest such that its north pole is very close to the right end of a coil of wire attached to a meter, as shown below.
In order to generate an electrical current registered by the meter, you could
i. move the magnet away from the coil at constant velocity
ii. move the magnet into the coil at constant velocity
iii. accelerate the magnet into the coil
iv. increase the area of the coil
v. do nothing - the meter is already registering a current
(A) $\mathrm{i}$
(B) i and ii
(C) i, ii and iii
(D) i, ii, iii and iv
(E) i, ii, iii, iv and $\mathrm{v}$

Vishal Gupta
Vishal Gupta
Numerade Educator
01:09

Problem 14

A current of 7 amps is flowing around the loop shown above. If the magnetic field strength is $0.2 \mathrm{~T}$ and the hypotenuse has length $70 \mathrm{~cm}$, the force on it is closest to
(A) $0.14 \mathrm{~N}$
(B) $0.48 \mathrm{~N}$
(C) $0.98 \mathrm{~N}$
(D) $1.44 \mathrm{~N}$
(E) $1.92 \mathrm{~N}$

Raj Bala
Raj Bala
Numerade Educator
00:46

Problem 15

The direction of the force on the hypotenuse is
(A) pointed to the north.
(B) to the south.
(C) pointed to the northwest.
(D) pointed to the southeast.
(E) pointed to the southwest.

Keshav Singh
Keshav Singh
Numerade Educator
01:24

Problem 16

A current $l$ is flowing counterclockwise in a circular loop in a uniform $B$-field, as shown in the figure.
At 4:00 in the diagram, the magnetic force on the loop is pointed in which direction?
(A) Into the page
(B) Out of the page
(C) Towards 10:00
(D) Towards 12:00
(E) Towards 6:00

Ankur S
Ankur S
Numerade Educator
01:41

Problem 17

Two positive charges of magnitude $q$ and $2 q$ are fixed in place along the $x$-axis. Is there any place along the $x$-axis where the total field could be zero?
(A) Yes, somewhere to the left of the charge $q$
(B) Yes, somewhere to the right of the charge $2 q$
(C) Yes, between the two charges but closer to $q$
(D) Yes, between the two charges but closer to $2 q$
(E) No, the field can never be zero

RZ
Rubeena Zulfiqar
Numerade Educator
10:37

Problem 18

The signs of both charges in the previous problem are changed from positive to negative. Is there any point along the $x$-axis where the electric field could be zero?
(A) Yes, somewhere to the left of the charge marked $q$
(B) Yes, somewhere to the right of the charge marked $2 q$
(C) Yes, between the two charges but closer to $q$
(D) Yes, between the two charges but closer to $2 q$
(E) No, the field can never be zero

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:48

Problem 19

The sign of $q$ remains positive and the sign of $2 q$ is changed to negative. Is there any point along the $x$-axis where the electric field could be zero?
(A) Yes, somewhere to the left of the charge marked $q$
(B) Yes, somewhere to the right of the charge marked $2 q$
(C) Yes, between the two charges but closer to $q$
(D) Yes, between the two charges but closer to $2 q$
(E) No, the field can never be zero

Athiru Pathiraja
Athiru Pathiraja
Numerade Educator
01:56

Problem 20

Two long, parallel wires separated by a distance $r$ carry equal currents $I$ in opposite directions, as shown. The direction of the field caused by the top wire at the position of the bottom wire and the direction of the force exerted by the top wire on the bottom wire are
(A) $B$ into the page; $F$ down
(B) $B$ up; $F$ into the page
(C) $B$ into the page; $F$ up
(D) $B$ out of the page; $F$ down
(E) $B$ down; $F$ out of the page

Vishal Gupta
Vishal Gupta
Numerade Educator
01:27

Problem 21

In the previous problem, the direction of the magnetic field produced by the bottom wire and the direction of the force exerted by the bottom wire on the top wire are
(A) $B$ into the page; $F$ down
(B) $B$ up; $F$ into the page
(C) $B$ into the page; $F$ up
(D) $B$ out of the page; $F$ down
(E) $B$ out of the page; $F$ up

Paul Gabriel
Paul Gabriel
Numerade Educator
01:16

Problem 22

The two wires in the previous problem each carry 1 amp of current and are separated by a distance $r=1 \mathrm{~m}$. The force per meter between the two wires is
(A) $4 \pi \times 10^{-2} \mathrm{~N} / \mathrm{m}$
(B) $2 \times 10^{-4} \mathrm{~N} / \mathrm{m}$
(C) $4 \pi \times 10^{-7} \mathrm{~N} / \mathrm{m}$
(D) $2 \pi \times 10^{-7} \mathrm{~N} / \mathrm{m}$
(E) $2 \times 10^{-7} \mathrm{~N} / \mathrm{m}$

Ajay Singhal
Ajay Singhal
Numerade Educator
02:18

Problem 23

Two positive charges with magnitude $q$ and $2 q$ sit at points $(1,0)$ and $(0,1)$ on the $x$ - and $y$-axis, respectively. Which figure best represents the total electric field at the origin?
(A) $\mathrm{A}$
(B) $\mathrm{B}$
(C) $\mathrm{C}$
(D) $\mathrm{D}$
(E) $\mathrm{E}$

Vishal Gupta
Vishal Gupta
Numerade Educator
02:18

Problem 24

Two negative charges with magnitude $q$ and $2 q$ sit at points $(1,0)$ and $(0,1)$ on the $x$ - and $y$-axis, respectively. Which figure best represents the total electric field at the origin?
(A) $\mathrm{A}$
(B) $\mathrm{B}$
(C) $\mathrm{C}$
(D) $\mathrm{D}$
(E) $\mathrm{E}$

Vishal Gupta
Vishal Gupta
Numerade Educator
02:18

Problem 25

A negative charge with magnitude $q$ and a positive charge with magnitude $2 q$ sit at points $(1,0)$ and $(0,1)$ on the $x$ - and $y$-axis, respectively. Which figure best represents the total electric field at the origin?
(A) A
(B) $\mathrm{B}$
(C) $\mathrm{C}$
(D) D
(E) $\mathrm{E}$

Vishal Gupta
Vishal Gupta
Numerade Educator
07:10

Problem 26

Instead of a meter, a device (such as a battery) is attached to the coil that can generate a current. When the device is turned on the bar magnet will
(A) remain at rest.
(B) be attracted to the coil.
(C) be repelled from the coil.
(D) shoot through the coil.
(E) (B) or (C) depending on which way the current is flowing in the coil

Vishal Gupta
Vishal Gupta
Numerade Educator
01:30

Problem 27

The magnet is at rest far to the right and then shot into the coil with an initial speed $v$. As the magnet approaches the coil it will
(A) keep moving at speed $v$.
(B) slow down.
(C) speed up.
(D) gain potential energy.
(E) lose potential energy.

Hunza Gilgit
Hunza Gilgit
Numerade Educator
01:20

Problem 28

A particle of mass $m$ and charge $+q$ is shot with velocity $\mathbf{v}$ into a region of uniform magnetic field $\mathbf{B}$. Suppose that $\mathbf{v}$ points to the top of the page and $\mathbf{B}$ points out of the page. Ignoring gravity, the particle
(A) travels in a straight line.
(B) moves clockwise in a circle with radius $r=q B / m v$.
(C) moves counterclockwise in a circle with radius $r=q B / m v$.
(D) moves clockwise in a circle with radius $r=m v / q B$.
(E) moves counterclockwise in a circle with radius $r=m v / q B$.

Mayukh Banik
Mayukh Banik
Numerade Educator
00:46

Problem 29

Proton $A$ is moving with speed $10^6 \mathrm{~m} / \mathrm{s}$ in a magnetic field of $0.01 \mathrm{~T}$. Proton $B$ is moving in the same magnetic field with speed $2 \times 10^6 \mathrm{~m} / \mathrm{s}$. One can conclude that
(A) Both protons have an orbital radius of about 1 meter.
(B) Both protons have the same orbital period of about $6.5 \times 10^{-6} \mathrm{~s}$.
(C) proton $B$ has twice the orbital period of proton $A$.
(D) proton $B$ has twice the orbital frequency of proton $A$.
(E) proton $B$ has half the orbital radius of proton $B$.

Hast Aggarwal
Hast Aggarwal
Numerade Educator
05:33

Problem 30

A conducting ring is dropped through a region of constant $B$-field, as shown.
As the ring falls through the $B$-field, an electrical current is induced in the ring that
(A) flows counterclockwise at the top, is zero in the center and flows clockwise at the bottom.
(B) flows clockwise at every position.
(C) flows counterclockwise at every position.
(D) flows clockwise at the top, is zero in the center and flows counterclockwise at the bottom.
(E) is always zero.

Mark J
Mark J
Numerade Educator
01:53

Problem 31

Two wire loops, 1 and 2 , are moving with equal speeds in the directions indicated below relative to a very long wire carrying a current $I$.
Which statements are true about the loops? (More than one answer allowed.)
i. A clockwise current is induced in loop 1; ii. A clockwise current is induced in loop 2 ;
iii. A counterclockwise current is induced in loop 1; iv. A counterclockwise current is induced in loop 2;
v. Zero current is induced in loop 1; vi. Zero current is induced in loop 2

Vishal Gupta
Vishal Gupta
Numerade Educator
01:46

Problem 32

A circular loop rotates around a horizontal axis coming out of the page (side view shown, below). The loop is rotating in a uniform $B$-field, pointed downward.
For every two full rotations, how often does the induced current change direction?
(A) Twice
(B) Four times
(C) Eight times
(D) Twelve time
(E) Sixteen times

Prabhu Ramji
Prabhu Ramji
Numerade Educator
01:11

Problem 33

Two oppositely charged parallel plates are held apart at distance of $10 \mathrm{~cm}$. The potential difference between them is maintained at 50 volts. The electric field between them is
(A) $5 \mathrm{~V} / \mathrm{m}$, down
(B) $50 \mathrm{~V} / \mathrm{m}$, up
(C) $500 \mathrm{~V} / \mathrm{m}$, down
(D) $500 \mathrm{~V} / \mathrm{m}$, up
(E) $1 / 50 \mathrm{~V} / \mathrm{m}$, down

Yuva S
Yuva S
Numerade Educator
01:09

Problem 34

A test charge $+q$ and a test charge $-q$ are released midway between the two plates. Let the voltage of the top plate be $V$ and the voltage of the bottom plate be 0 . The distance between the two plates is $d$. Which of the following statements about the test charges are true?
i. Both charges have gained a kinetic energy of $|q| E d / 2$ when they hit the plates.
ii. Charge $+q$ is initially at a positive voltage and charge $-q$ is initially at a negative voltage.
iii. Charge $+q$ initially has a positive potential energy and charge $-q$ initially has a negative potential energy.
iv. Both charges lose potential energy.
(A) i only
(B) i and ii
(C) i and iii
(D) iii and iv
(E) i, iii and iv

Prem Bijarniya
Prem Bijarniya
Numerade Educator
17:38

Problem 35

At what initial velocity $v_o$ must an electron be shot off from the top plate in order to reach the bottom plate?
(A) $2.1 \times 10^3 \mathrm{~m} / \mathrm{s}$
(B) $2.1 \times 10^5 \mathrm{~m} / \mathrm{s}$
(C) $4.2 \times 10^6 \mathrm{~m} / \mathrm{s}$
(D) $0 \mathrm{~m} / \mathrm{s}$
(E) $4.2 \times 10^8 \mathrm{~m} / \mathrm{s}$

Linda Winkler
Linda Winkler
Numerade Educator
02:43

Problem 36

What potential difference between the two plates would be needed to accelerate a hydrogen ion (a proton) from rest to a speed of $10^6 \mathrm{~m} / \mathrm{s}$ ?
(A) $100 \mathrm{~V}$
(B) $500 \mathrm{~V}$
(C) $1000 \mathrm{~V}$
(D) $5000 \mathrm{~V}$
(E) $10,000 \mathrm{~V}$

Mayank Tripathi
Mayank Tripathi
Numerade Educator
02:59

Problem 37

The voltage in the previous problems is maintained at $50 \mathrm{~V}$. An uncharged copper block of thickness $2 \mathrm{~cm}$ and length equal to that of the plates is inserted exactly midway between them. What is the field strength between the bottom of the copper block and the bottom plate?
(A) $0 \mathrm{~V} / \mathrm{m}$
(B) $250 \mathrm{~V} / \mathrm{m}$
(C) $500 \mathrm{~V} / \mathrm{m}$
(D) $625 \mathrm{~V} / \mathrm{m}$
(E) $2000 \mathrm{~V} / \mathrm{m}$

Sheh Lit Chang
Sheh Lit Chang
University of Washington
01:15

Problem 38

Metal sphere $A$ has a radius of $5 \mathrm{~cm}$ and metal sphere $B$ has a radius of $10 \mathrm{~cm}$. Sphere $A$ carries a charge of $9 \mathrm{nC}$ and sphere $B$ carries a charge of $18 \mathrm{nC}$. If the surfaces of $A$ and $B$ are $185 \mathrm{~cm}$ apart, the potential energy between them is
(A) $7.29 \times 10^{-17} \mathrm{~J}$
(B) $7.88 \times 10^{-9} \mathrm{~J}$
(C) $7.88 \times 10^{-7} \mathrm{~J}$
(D) $7.29 \times 10^{-9} \mathrm{~J}$
(E) None of the above

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
01:27

Problem 39

A third sphere carrying a charge of $9 \mathrm{nC}$ is brought to $2 \mathrm{~m}$ of the center of sphere $A$ in the previous problem and to $3 \mathrm{~m}$ of the center of sphere $B$. The total potential energy of the system is now
(A) $1.58 \times 10^{-9} \mathrm{~J}$
(B) $7.29 \times 10^{-7} \mathrm{~J}$
(C) $1.21 \times 10^{-6} \mathrm{~J}$
(D) $1.58 \times 10^{-6} \mathrm{~J}$
(E) $1.58 \times 10^{-5} \mathrm{~J}$

Yuva S
Yuva S
Numerade Educator
02:57

Problem 40

Two masses of $10^{-9} \mathrm{~kg}$ each carry a charge of $+3 \mathrm{nC}$ and are initially held motionless by a massless thread at a distance of $9 \mathrm{~m}$.
a) Draw the electric field produced by the two charges.
b) What is the tension in the thread?
c) The thread is cut by a magic wand. What is the initial acceleration of each of the charges?
d) How does the acceleration change with $r$ ? Graph the behavior. Explain qualitatively how the velocity will change with $r$. In particular, what happens to the velocity when $r$ goes to infinity. Where is the maximum velocity?

Yanlian Xin
Yanlian Xin
Numerade Educator
05:54

Problem 41

Two identical plastic balls of mass $10 \mathrm{gm}$ each are hung by threads with length $30 \mathrm{~cm}$ from a common point, as shown below.
The balls are each charged with the same charge $q$ and repel each other until they come to rest with a horizontal separation of $30 \mathrm{~cm}$.
a) Sketch the electric field produced by the two balls.
b) Draw the force vectors on the right-hand ball.
c) What is the charge $q$ in each ball?

Surendra Kumar
Surendra Kumar
Numerade Educator
07:42

Problem 42

A proton is launched from a very long negatively charged plate at an initial velocity $v_o$ and angle $\theta$ toward an identical, positively charged plate, as shown below.
The two plates are held at a potential difference $V=1000$ volts, and the distance between the two plates is $d$.
a) Draw in the electric field vectors. Write an algebraic expression for the electric field strength in terms of given quantities.
b) If $v_o=4 \times 10^5 \mathrm{~m} / \mathrm{s}$, and $\theta=60^{\circ}$, does $--_{-}--_{-}--_{-}--^{-}$ the proton hit the top plate? If so, with what velocity?
c) If $d=25 \mathrm{~cm}$, how long is the proton in flight?
d) If a uniform magnetic field pointing along the proton's initial velocity vector is introduced between the plates, does this alter the conclusion to (b)?

Janielle Madlansacay
Janielle Madlansacay
Numerade Educator
05:33

Problem 43

The Millikan oil-drop experiment was the first experiment that attempted to determine the charge on the electron. Today students perform modern versions of the experiment in various ways, usually involving small latex spheres. The spheres are injected between two conducting plates held at a potential difference $V$. Assume that the plates themselves are contained in a vacuum chamber.
The spheres are of identical mass but may carry different and unknown amounts of charge. The voltage is adjusted until a selected sphere rises a constant velocity and the calculated charge on the sphere is recorded. This procedure is repeated many times for many different spheres. Eventually a graph of the results is produced:
a) Write down the condition that the spheres rise with constant velocity as a function of voltage and charge.
b) What shape should the theoretical curve of the charge versus the voltage be?
c) How might you physically account for the lack of data between $1000 \mathrm{~V}$ and $2000 \mathrm{~V}$ ?
d) If the distance between the plates is $5 \mathrm{~cm}$, what is the mass of the latex spheres?

Keshav Singh
Keshav Singh
Numerade Educator
02:12

Problem 44

A conducting wire of length $0.5 \mathrm{~m}$ and mass $10 \mathrm{gm}$ is suspended in a uniform magnetic field of $0.5 \mathrm{~T}$ by two identical conducting springs with spring constant $k$ (see below).
A current of $1 \mathrm{amp}$ is sent through the springs and wire, and the wire is observed to move downward $1 \mathrm{~cm}$, stretching the springs.
a) In which direction is the current flowing?
b) Derive an expression for the spring constant in terms of known quantities and fundamental constants.
c) What is the numerical value of $k$ ?

Caitlyn Axe
Caitlyn Axe
Numerade Educator
02:09

Problem 45

Until recently, TV sets consisted of what was called a cathode-ray tube. Electrons were boiled off a light bulb filament and passed through plates that deflected the particles; the electron beam went on to strike the TV screen itself and lit up a pixel of phosphor. The beam could be deflected both up and down and sideways (only one direction shown). By deflecting the electron beam and scanning it across the screen a picture was built up. Consider the simplified TV below.
An electron beam is shot along the centerline between the two deflector plates. The top plate is held by a power supply (not shown) at a voltage $V=$ $+1000$ volts above the bottom plate. The separation between the plates is $d=4 \mathrm{~cm}$. The length of the plates is $\ell=8 \mathrm{~cm}$. The distance $L$ from the end of the deflector plate to the TV screen is $30 \mathrm{~cm}$. The electrons enter the region between the deflector plates with a velocity $v=4 \times 10^7 \mathrm{~m} / \mathrm{s}$.
a) In which direction is the electric field between the deflector plates?
b) In which direction are the electrons deflected?
c) What is the force on an electron? (Neglect gravity.)
d) What is the acceleration on the electron?
e) What is the total deflection of the electron as it hits the TV screen?
f) What size magnetic field and in what direction would you need to place between the deflector plates in order to prevent the electrons from being deflected?

Dominador Tan
Dominador Tan
Numerade Educator
05:57

Problem 46

Four charges of equal magnitude are arranged in a square in two configurations, as shown below. The side length of the square is $s$.
a) What is the magnitude and direction of the electric field at the center of the square in configuration
(a)?
b) What is the magnitude and direction of the electric field at the center of the square in configuration
(b)?
c) If the top left charge in (a) is removed, what is the electric field (magnitude and direction) at that point due to the other three charges?
d) What is the total potential energy of configuration (a) with all four charges present?
e) What is the total potential energy of configuration (b) with all four charges present?
f) For which configuration would it take more work to remove the charge from the lower right corner to an infinite distance from the square?

Vishal Gupta
Vishal Gupta
Numerade Educator
12:08

Problem 47

A vertical wire carries a current $I_1$ up in the plane of the page, as shown below. A square wire loop with side length $L$ sits in the plane of the page at a distance $b$ from the wire and carries a current $I_2$ in the counterclockwise direction.
a) Is there a net force on the loop? If so, in what direction?
b) Is there a net torque on the loop around a vertical axis running through the loop's center? If so, what is its action on the loop?
c) If $I_1=2 \mathrm{~A} ; I_2=1 \mathrm{~A} ; b=10 \mathrm{~cm} ; L=5 \mathrm{~cm}$, what is the magnitude of the net force?
d) What is the magnitude of the net torque?

Jayashree Behera
Jayashree Behera
Numerade Educator
08:47

Problem 48

A mass spectrometer is a device for measuring the mass of atomic isotopes. As shown below, it consists of a small accelerator, which accelerates singly-ionized atoms across a voltage $V$. (Singly-ionized atoms have had one electron removed.) The ions are injected into a region with a constant magnetic field $\mathbf{B}$ (here pointing out of the page).
a) Assuming the ions are accelerated from rest, with what velocity $v$ are they injected into the magnetic field? (Write $v$ in terms of the voltage $V$, the charge on the ion $q$ and the ion's mass m.)
b) What is the magnitude and direction of the force $\mathbf{F}$ acting on the ions?
c) On the diagram, draw the trajectory that the ions follow.
d) Write an algebraic expression involving the above that gives the distance $d$ from their point of entry where the ions end up.
e) You are given a sample consisting of ${ }^{24} \mathrm{Mg}$ and ${ }^{26} \mathrm{Mg}$ (magnesium). The former atoms have mass $m=3.983 \times 10^{-26} \mathrm{~kg}$. If $V=2500 \mathrm{~V}, B=556 \mathrm{G}$, how far apart will the atoms end up?

Ceren Uzun
Ceren Uzun
Texas Tech University
05:34

Problem 49

A rectangular loop is situated in a region with a uniform magnetic field of $0.1 \mathrm{~T}$ pointing into the page, as shown below. The length of the loop is $20 \mathrm{~cm}$ and the width is $10 \mathrm{~cm}$.
a) What is the magnetic flux through the loop?
b) If the value of $B$ is increased from $0.1 \mathrm{~T}$ to $0.5 \mathrm{~T}$ in $0.3 \mathrm{~s}$, what will be the EMF induced into the loop? What will be the direction of the induced current? Justify your answer.
c) If the resistance of the loop is $R=1 \Omega$, what is the value of the current?
d) If the $B$-field is tilted at an angle $\theta=15^{\circ}$ from the normal to the page, what is the flux through the loop?
e) Give two ways that one could change the induced EMF in the loop, other than changing $B$.
f) Draw a rotation axis from left to right in the plane of the page that passes through the loop's center. The loop is rotated about this axis at a constant angular velocity. Write an expression for the flux in terms of the angular velocity $\omega$ and the time $t$.

Vishal Gupta
Vishal Gupta
Numerade Educator
02:55

Problem 50

The rail gun, currently being developed by the US Navy, is a weapon designed to shoot a projectile off a set of rails by electromagnetic means. Consider a simplified version of the gun, below.
A power supply (box) sends a current $I$ around a circuit consisting of two frictionless rails (horizontal lines) and through a projectile (vertical bar) of length $\ell$ and mass $m$. The total length of the rails is $L$. A uniform magnetic field, $B$, covering the entire area of the system, is directed into the page.
e) If $L=10 \mathrm{~m} ; \ell=0.1 \mathrm{~m} ; m=2 \mathrm{~kg} ; I=10^4 \mathrm{~A}$, what is the launch speed of the projectile?

Ajay Singhal
Ajay Singhal
Numerade Educator
05:18

Problem 51

A wire carries a current of $I=10 \mathrm{~A}$ into the page. With a magnetic field probe, a student measures the $B$-field at five points and notes down the results: $(1,2.2) ;(2,0.85) ;(5,0.35) ;(8,0.31) ;(10,0.11)$. The first number in each pair is the distance to the right of the wire in $\mathrm{cm}$ and the second number is the $B$-field in units of $10^{-4} \mathrm{~T}$.
a) Plot the data, then plot the expected curve on the same graph.
b) What would you say is the average error of the measurements?
c) After you have plotted the data, someone reports that the earth's $B$-field at this location is $0.5$ gauss, pointing to the top of the page. Replot the corrected $B$-field.
d) What percentage error does the earth's field introduce to the measurements as a function of $r$ ?
e) Would you say the original results were trustworthy?

Amit Srivastava
Amit Srivastava
Numerade Educator
02:07

Problem 52

A solid copper sphere of radius $R=10 \mathrm{~cm}$ carries a charge of $+5 \mathrm{nC}$.
a) Give an algebraic expression for the electric field at all distances $r<R$. What is the numerical value of the field at $r=5 \mathrm{~cm}$ ?
b) Give an algebraic expression for the electric potential at all distances $r<R$. What is the numerical value of the potential at $r=5 \mathrm{~cm}$ ?
c) Sketch a graph of both the field and potential for $r \geq 0$.
d) A second, uncharged copper sphere of radius $r=5 \mathrm{~cm}$ is brought near the first sphere. Graph the electric potential everywhere from $0 \leq r \leq \infty$.

Ajay Singhal
Ajay Singhal
Numerade Educator