Physics

John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler

Chapter 19

Electric Potential Energy and the Electric Potential - all with Video Answers

Educators

Chapter Questions

Problem 1

During a particular thunderstorm, the electric potential difference between a cloud and the ground is $V_{\text {cloud }}-V_{\text {ground }}=1.3 \times 10^{8} \mathrm{V},$ with the cloud being at the higher potential. What is the change in an electron's electric potential energy when the electron moves from the ground to the cloud?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 2

A particle with a charge of $-1.5 \mu \mathrm{C}$ and a mass of $2.5 \times 10^{-6} \mathrm{kg}$ is released from rest at point $A$ and accelerates toward point $B$, arriving there with a speed of $42 \mathrm{m} / \mathrm{s} .$ The only force acting on the particle is the electric force.
(a) Which point is at the higher potential? Give your reasoning.
(b) What is the potential difference $V_{\mathrm{B}}-V_{\mathrm{A}}$ between $\mathrm{A}$ and $\mathrm{B} ?$

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Joseph Peters

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Problem 3

Suppose that the electric potential outside a living cell is higher than that inside the cell by 0.070 V. How much work is done by the electric force when a sodium ion (charge $=+e$ ) moves from the outside to the inside?

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Problem 4

A particle has a charge of $+1.5 \mu \mathrm{C}$ and moves from point $A$ to point $B,$ a distance of $0.20 \mathrm{m}$. The particle experiences a constant electric force, and its motion is along the line of action of the force. The difference between the particle's electric potential energy at $A$ and at $B$ is $\mathrm{EPE}_{A}-\mathrm{EPE}_{B}=$ $+9.0 \times 10^{-4} \mathrm{J} .$ (a) Find the magnitude and direction of the electric force that acts on the particle.
(b) Find the magnitude and direction of the electric field that the particle experiences.

Khoobchandra Agrawal

Khoobchandra Agrawal

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Problem 5

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Ajay Singhal

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Problem 6

Review Multiple-Concept Example 4 to see the concepts that are pertinent here. In a television picture tube, electrons strike the screen after being accelerated from rest through a potential difference of $25000 \mathrm{V}$. The speeds of the electrons are quite large, and for accurate calculations of the speeds, the effects of special relativity must be taken into account. Ignoring such effects, find the electron speed just before the electron strikes the screen.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 7

Multiple-Concept Example 4 deals with the concepts that are important in this problem. As illustrated in Figure $19.5 b$, a negatively charged particle is released from rest at point $B$ and accelerates until it reaches point $A$. The mass and charge of the particle are $4.0 \times 10^{-6} \mathrm{kg}$ and $-2.0 \times 10^{-5} \mathrm{C},$ respectively. Only the gravitational force and the electrostatic force act on the particle, which moves on a horizontal straight line without rotating. The electric potential at $A$ is $36 \mathrm{V}$ greater than that at $B ;$ in other words, $V_{A}-V_{B}=$ $36 \mathrm{V}$. What is the translational speed of the particle at point $A ?$

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Problem 8

An electron and a proton, starting from rest, are accelerated through an electric potential difference of the same magnitude. In the process, the electron acquires a speed $v_{\mathrm{e}},$ while the proton acquires a speed $v_{\mathrm{p}}$ Find the ratio $v_{\mathrm{c}} / v_{\mathrm{p}}$.

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Joseph Peters

Numerade Educator

Problem 9

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Ajay Singhal

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Problem 10

A moving particle encounters an external electric field that decreases its kinetic energy from $9520 \mathrm{eV}$ to $7060 \mathrm{eV}$ as the particle moves from position $A$ to position $B .$ The electric potential at $A$ is $-55.0 \mathrm{V},$ and the electric potential at $B$ is +27.0 V. Determine the charge of the particle. Include the algebraic sign $(+$ or $-$ ) with your answer.

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Joseph Peters

Numerade Educator

Problem 11

During a lightning flash, there exists a potential difference of $V_{\text {cloud }}-V_{\text {ground }}=1.2 \times 10^{9} \mathrm{V}$ between a cloud and the ground. As a result, a charge of $-25 \mathrm{C}$ is transferred from the ground to the cloud. (a) How much work $W_{\text {ground-cloud }}$ is done on the charge by the electric force? (b) If the work done by the electric force were used to accelerate a 1100 -kg automobile from rest, what would be its final speed? (c) If the work done by the electric force were converted into heat, how many kilograms of water at $0^{\circ} \mathrm{C}$ could be heated to $100^{\circ} \mathrm{C} ?$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 12

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Ajay Singhal

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Problem 13

Two point charges, $+3.40 \mu \mathrm{C}$ and $-6.10 \mu \mathrm{C},$ are separated by $1.20 \mathrm{m}$ What is the electric potential midway between them?

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Problem 14

An electron and a proton are initially very far apart (effectively an infinite distance apart). They are then brought together to form a hydrogen atom, in which the electron orbits the proton at an average distance of $5.29 \times$ $10^{-11} \mathrm{m} .$ What is $\mathrm{EPE}_{\text {final }}-\mathrm{EPE}_{\text {initial }},$ which is the change in the electric potential energy?

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Joseph Peters

Numerade Educator

Problem 15

Two charges $A$ and $B$ are fixed in place, at different distances from a certain spot. At this spot the potentials due to the two charges are equal. Charge A is 0.18 $\mathrm{m}$ from the spot, while charge $\mathrm{B}$ is $0.43 \mathrm{m}$ from it. Find the ratio $q_{\mathrm{B}} / q_{\mathrm{A}}$ of the charges.

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Problem 16

The drawing shows a square, each side of which has a length of $L=0.25 \mathrm{m} .$ On two corners of the square are fixed different positive charges, $q_{1}$ and $q_{2} .$ Find the electric potential energy of a third charge $q_{3}=-6.0 \times 10^{-9} \mathrm{C}$ placed at corner $A$ and then at corner $B$.

Anand Jangid

Numerade Educator

Problem 17

The drawing shows four point charges. The value of $q$ is $2.0 \mu \mathrm{C}$, and the distance $d$ is $0.96 \mathrm{m}$. Find the total potential at the location $P .$ Assume that the potential of a point charge is zero at infinity.

Dominador Tan

Numerade Educator

Problem 18

A charge of $+125 \mu \mathrm{C}$ is fixed at the center of a square that is $0.64 \mathrm{m}$ on a side. How much work is done by the electric force as a charge of $+7.0 \mu \mathrm{C}$ is moved from one corner of the square to any other empty corner? Explain.

Ren Jie Tuieng

Numerade Educator

Problem 19

The drawing shows six point charges arranged in a rectangle. The value of $q$ is $9.0 \mu \mathrm{C},$ and the distance $d$ is $0.13 \mathrm{m} .$ Find the total electric potential at location $P,$ which is at the center of the rectangle.

Sheh Lit Chang

University of Washington

Problem 20

Location $A$ is $3.00 \mathrm{m}$ to the right of a point charge $q .$ Location $B$ lies on the same line and is $4.00 \mathrm{m}$ to the right of the charge. The potential difference between the two locations is $V_{B}-V_{A}=45.0 \mathrm{V} .$ What are the magnitude and sign of the charge?

Ren Jie Tuieng

Numerade Educator

Problem 21

Identical $+1.8 \mu \mathrm{C}$ charges are fixed to adjacent corners of a square. What charge (magnitude and algebraic sign) should be fixed to one of the empty corners, so that the total electric potential at the remaining empty corner is $0 \mathrm{V} ?$

Khoobchandra Agrawal

Khoobchandra Agrawal

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Problem 22

Charges of $-q$ and $+2 q$ are fixed in place, with a distance of $2.00 \mathrm{m}$ between them. A dashed line is drawn through the negative charge, perpendicular to the line between the charges. On the dashed line, at a distance $L$ from the negative charge, there is at least one spot where the total potential is zero. Find $L$.

Kenny Mesadieu

Numerade Educator

Problem 23

Determine the electric potential energy for the array of three charges in the drawing, relative to its value when the charges are infinitely far away and infinitely far apart.

Sheh Lit Chang

University of Washington

Problem 24

Two identical point charges $\left(q=+7.20 \times 10^{-6} \mathrm{C}\right)$ are fixed at diagonally opposite corners of a square with sides of length $0.480 \mathrm{m}$. A test charge $\left(q_{0}=-2.40 \times 10^{-8} \mathrm{C}\right),$ with a mass of $6.60 \times 10^{-8} \mathrm{kg},$ is released from rest at one of the empty corners of the square. Determine the speed of the test charge when it reaches the center of the square.

Ren Jie Tuieng

Numerade Educator

Problem 25

Two protons are moving directly toward one another. When they are very far apart, their initial speeds are $3.00 \times 10^{6} \mathrm{m} / \mathrm{s} .$ What is the distance of closest approach?

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Problem 26

Four identical charges $(+2.0 \mu \mathrm{C}$ each $)$ are brought from infinity and fixed to a straight line. The charges are located $0.40 \mathrm{m}$ apart. Determine the electric potential energy of this group.

Chasen Shaw

Numerade Educator

Problem 27

A charge of $-3.00 \mu \mathrm{C}$ is fixed in place. From a horizontal distance of $0.0450 \mathrm{m},$ a particle of $\operatorname{mass} 7.20 \times 10^{-3} \mathrm{kg}$ and charge $-8.00 \mu \mathrm{C}$ is fired with an initial speed of $65.0 \mathrm{m} / \mathrm{s}$ directly toward the fixed charge. How far does the particle travel before its speed is zero?

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Problem 28

Identical point charges of $+1.7 \mu \mathrm{C}$ are fixed to diagonally opposite corners of a square. A third charge is then fixed at the center of the square, such that it causes the potentials at the empty corners to change signs without changing magnitudes. Find the sign and magnitude of the third charge.

Ren Jie Tuieng

Numerade Educator

Problem 29

One particle has a mass of $3.00 \times 10^{-3} \mathrm{kg}$ and a charge of $+8.00 \mu \mathrm{C}$. A second particle has a mass of $6.00 \times 10^{-3} \mathrm{kg}$ and the same charge. The two particles are initially held in place and then released. The particles fly apart, and when the separation between them is $0.100 \mathrm{m},$ the speed of the $3.00 \times 10^{-3} \mathrm{kg}$ particle is $125 \mathrm{m} / \mathrm{s} .$ Find the initial separation between the particles.

Dominador Tan

Numerade Educator

Problem 30

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Ajay Singhal

Numerade Educator

Problem 31

Two equipotential surfaces surround a $+1.50 \times 10^{-8} \mathrm{C}$ point charge. How far is the $190-\mathrm{V}$ surface from the $75.0-\mathrm{V}$ surface?

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Problem 32

An equipotential surface that surrounds a point charge $q$ has a potential of $490 \mathrm{V}$ and an area of $1.1 \mathrm{m}^{2} .$ Determine $q$.

Ren Jie Tuieng

Numerade Educator

Problem 33

The inner and outer surfaces of a cell membrane carry a negative and a positive charge, respectively. Because of these charges, a potential difference of about $0.070 \mathrm{V}$ exists across the membrane. The thickness of the cell membrane is $8.0 \times 10^{-9} \mathrm{m} .$ What is the magnitude of the electric field in the membrane?

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Problem 34

A positive point charge $\left(q=+7.2 \times 10^{-8} \mathrm{C}\right)$ is surrounded by an equipotential surface $A,$ which has a radius of $r_{A}=1.8 \mathrm{m} .$ A positive test charge $\left(q_{0}=+4.5 \times 10^{-11} \mathrm{C}\right)$ moves from surface $A$ to another equipotential surface $B,$ which has a radius $r_{B} .$ The work done as the test charge moves from surface $A$ to surface $B$ is $W_{A B}=-8.1 \times 10^{-9}$ J. Find $r_{B}$.

Ren Jie Tuieng

Numerade Educator

Problem 35

A spark plug in an automobile engine consists of two metal conductors that are separated by a distance of $0.75 \mathrm{mm} .$ When an electric spark jumps between them, the magnitude of the electric field is $4.7 \times$ $10^{7} \mathrm{V} / \mathrm{m} .$ What is the magnitude of the potential difference $\Delta V$ between the conductors?

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Problem 36

The drawing that accompanies Problem 60 shows a graph of a set of equipotential surfaces in cross section. The grid lines are $2.0 \mathrm{cm}$ apart. Determine the magnitude and direction of the electric field at position $D$. Specify whether the electric field points toward the top or the bottom of the drawing.

Ren Jie Tuieng

Numerade Educator

Problem 37

An electric field has a constant value of $4.0 \times 10^{3} \mathrm{V} / \mathrm{m}$ and is directed downward. The field is the same everywhere. The potential at a point $P$ within this region is 155 V. Find the potential at the following points:
(a) $6.0 \times 10^{-3} \mathrm{m}$ directly above $P,($
(b) $3.0 \times 10^{-3} \mathrm{m}$ directly below $P$
(c) $8.0 \times 10^{-3} \mathrm{m}$ directly to the right of $P$

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Problem 38

An electron is released from rest at the negative plate of a parallel plate capacitor and accelerates to the positive plate (see the drawing). The plates are separated by a distance of $1.2 \mathrm{cm},$ and the electric field within the capacitor has a magnitude of $2.1 \times 10^{6} \mathrm{V} / \mathrm{m} .$ What is the kinetic energy of the electron just as it reaches the positive plate?

Ren Jie Tuieng

Numerade Educator

Problem 39

The drawing shows the electric potential as a function of distance along the $x$ axis. Determine the magnitude of the electric field in the region (a) $A$ to $B,$ (b) $B$ to $C,$ and (c) $C$ to $D$.

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Problem 40

At a distance of $1.60 \mathrm{m}$ from a point charge of $+2.00 \mu \mathrm{C},$ there is an equipotential surface. At greater distances there are additional equipotential surfaces. The potential difference between any two successive surfaces is $1.00 \times 10^{3} \mathrm{V} .$ Starting at a distance of $1.60 \mathrm{m}$ and moving radially outward, how many of the additional equipotential surfaces are crossed by the time the electric field has shrunk to one-half of its initial value? Do not include thenstarting surface.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 41

The drawing shows a uniform electric field that points in the negative $y$ direction; the magnitude of the field is $3600 \mathrm{N} / \mathrm{C}$. Determine the electric potential difference
(a) $V_{B}-V_{A}$ between points $A$ and $B,$ (b) $V_{c}-V_{B}$ between points $B$ and $C$, and
(c) $V_{A}-V_{c}$ between points $C$ and $A$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 42

What is the capacitance of a capacitor that stores $4.3 \mu \mathrm{C}$ of charge on its plates when a voltage of $1.5 \mathrm{V}$ is applied between them?

Ren Jie Tuieng

Numerade Educator

Problem 43

The electric potential energy stored in the capacitor of a defibrillator is $73 \mathrm{J},$ and the capacitance is $120 \mu \mathrm{F}$. What is the potential difference that exists across the capacitor plates?

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Problem 44

Two identical capacitors store different amounts of energy: capacitor A stores $3.1 \times 10^{-3} \mathrm{J},$ and capacitor $\mathrm{B}$ stores $3.4 \times 10^{-4} \mathrm{J} .$ The voltage across the plates of capacitor B is 12 V. Find the voltage across the plates of capacitor A.

Ren Jie Tuieng

Numerade Educator

Problem 45

The electronic flash attachment for a camera contains a capacitor for storing the energy used to produce the flash. In one such unit, the potential difference between the plates of an $850-\mu \mathrm{F}$ capacitor is $280 \mathrm{V}$.
(a) Determine the energy that is used to produce the flash in this unit.
(b) Assuming that the flash lasts for $3.9 \times 10^{-3} \mathrm{s},$ find the effective power or "wattage" of the flash.

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Problem 46

The same voltage is applied between the plates of two different capacitors. When used with capacitor A, this voltage causes the capacitor to store $11 \mu \mathrm{C}$ of charge and $5.0 \times 10^{-5} \mathrm{J}$ of energy. When used with capacitor $\mathrm{B}$ which has a capacitance of $6.7 \mu \mathrm{F}$, this voltage causes the capacitor to store a charge that has a magnitude of $q_{\mathrm{B}} .$ Determine $q_{\mathrm{B}}$.

Ren Jie Tuieng

Numerade Educator

Problem 47

A parallel plate capacitor has a capacitance of $7.0 \mu \mathrm{F}$ when filled with a dielectric. The area of each plate is $1.5 \mathrm{m}^{2}$ and the separation between the plates is $1.0 \times 10^{-5} \mathrm{m} .$ What is the dielectric constant of the dielectric?

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Problem 48

Two capacitors are identical, except that one is empty and the other is filled with a dielectric $(\kappa=4.50) .$ The empty capacitor is connected to a $12.0-\mathrm{V}$ battery. What must be the potential difference across the plates of the capacitor filled with a dielectric so that it stores the same amount of electrical energy as the empty capacitor?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 49

'I'he membrane that surrounds a certain type of living cell has a surface area of $5.0 \times 10^{-9} \mathrm{m}^{2}$ and a thickness of $1.0 \times 10^{-8} \mathrm{m} .$ Assume that the
membrane behaves like a parallel plate capacitor and has a dielectric constant of $5.0 .$ (a) The potential on the outer surface of the membrane is $+60.0 \mathrm{mV}$ greater than that on the inside surface. How much charge resides on the outer surface? (b) If the charge in part (a) is due to positive ions (charge $+e$ ), how many such ions are present on the outer surface?

Khoobchandra Agrawal

Khoobchandra Agrawal

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Problem 50

Capacitor A and capacitor B both have the same voltage across their plates. However, the energy of capacitor A can melt $m$ kilograms of ice at $0^{\circ} \mathrm{C},$ while the energy of capacitor $\mathrm{B}$ can boil away the same amount of water at $100^{\circ} \mathrm{C} .$ The capacitance of capacitor $\mathrm{A}$ is $9.3 \mu \mathrm{F} .$ What is the capacitance of capacitor B?

Ren Jie Tuieng

Numerade Educator

Problem 51

What is the potential difference between the plates of a 3.3-F capacitor that stores sufficient energy to operate a $75-$ W light bulb for one minute?

Khoobchandra Agrawal

Khoobchandra Agrawal

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Problem 52

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Ajay Singhal

Numerade Educator

Problem 53

Review Conceptual Example 10 before attempting this problem. An empty capacitor is connected to a $12.0-\mathrm{V}$ battery and charged up. The capacitor is then disconnected from the battery, and a slab of dielectric material $(\kappa=2.8)$ is inserted between the plates. Find the amount by which the potential difference across the plates changes. Specify whether the change is an increase or a decrease.

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Problem 54

An empty parallel plate capacitor is connected between the terminals of a $9.0-\mathrm{V}$ battery and charged up. The capacitor is then disconnected from the battery, and the spacing between the capacitor plates is doubled. As a result of this change, what is the new voltage between the plates of the capacitor?

Ren Jie Tuieng

Numerade Educator

Problem 55

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Ajay Singhal

Numerade Educator

Problem 56

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Ajay Singhal

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Problem 57

An axon is the relatively long tail-like part of a neuron, or nerve cell. The outer surface of the axon membrane (dielectric constant $=5$, thickness $=1 \times 10^{-8} \mathrm{m}$ ) is charged positively, and the inner portion is charged negatively. Thus, the membrane is a kind of capacitor. Assuming that the membrane acts like a parallel plate capacitor with a plate area of $5 \times 10^{-6} \mathrm{m}^{2}$ what is its capacitance?

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Problem 58

Refer to Multiple-Concept Example 3 to review the concepts that are needed here. A cordless electric shaver uses energy at a rate of 4.0 W from a rechargeable 1.5-V battery. Each of the charged particles that the battery delivers to the shaver carries a charge that has a magnitude of $1.6 \times$ $10^{-19} \mathrm{C} .$ A fully charged battery allows the shaver to be used for its maximum operation time, during which $3.0 \times 10^{22}$ of the charged particles pass between the terminals of the battery as the shaver operates. What is the shaver's maximum operation time?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 59

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Ajay Singhal

Numerade Educator

Problem 60

The drawing shows a graph of a set of equipotential surfaces seen in cross section. Each is labeled according to its electric potential. A $+2.8 \times 10^{-7} \mathrm{C}$ point charge is placed at position $A .$ Find the work that is done on the point charge by the electric force when it is moved (a) from $A$ to $B$, and (b) from $A$ to $C$.

Ren Jie Tuieng

Numerade Educator

Problem 61

The work done by an electric force in moving a charge from point $A$ to point $B$ is $2.70 \times 10^{-3}$ J. The electric potential difference between the two points is $V_{A}-V_{B}=50.0 \mathrm{V} .$ What is the charge?

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Problem 62

Two capacitors have the same plate separation, but one has square plates and the other has circular plates. The square plates are a length $L$ on each side, and the diameter of the circular plate is $L$. The capacitors have the same capacitance because they contain different dielectric materials. The dielectric constant of the material between the square plates has a value of $\kappa_{\text {square }}=3.00 .$ What is the dielectric constant $\kappa_{\text {circle }}$ of the material between the circular plates?

Ren Jie Tuieng

Numerade Educator

Problem 63

Three point charges, $-5.8 \times 10^{-9} \mathrm{C},-9.0 \times 10^{-9} \mathrm{C},$ and $+7.3 \times$ $10^{-9} \mathrm{C},$ are fixed at different positions on a circle. The total electric potential at the center of the circle is -2100 V. What is the radius of the circle?

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Problem 64

Equipotential surface $A$ has a potential of $5650 \mathrm{V},$ while equipotential surface $B$ has a potential of 7850 V. A particle has a mass of $5.00 \times$ $10^{-2} \mathrm{kg}$ and a charge of $+4.00 \times 10^{-5} \mathrm{C} .$ The particle has a speed of $2.00 \mathrm{m} / \mathrm{s}$ on surface $A$. A nonconservative outside force is applied to the particle, and it moves to surface $B$, arriving there with a speed of $3.00 \mathrm{m} / \mathrm{s}$. How much work is done by the outside force in moving the particle from $A$ to $B ?$

Ren Jie Tuieng

Numerade Educator

Problem 65

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Ajay Singhal

Numerade Educator

Problem 66

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Ajay Singhal

Numerade Educator

Problem 67

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Ajay Singhal

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Problem 68

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Ajay Singhal

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Problem 69

The capacitance of an empty capacitor is $1.2 \mu \mathrm{F}$. The capacitor is connected to a $12-\mathrm{V}$ battery and charged up. With the capacitor connected to the battery, a slab of dielectric material is inserted between the plates. As a result, $2.6 \times 10^{-5} \mathrm{C}$ of additional charge flows from one plate, through the battery, and onto the other plate. What is the dielectric constant of the material?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 70

Particle 1 has a mass of $m_{1}=3.6 \times 10^{-6} \mathrm{kg},$ while particle 2 has a mass of $m_{2}=6.2 \times 10^{-6} \mathrm{kg} .$ Each has the same electric charge. These particles are initially held at rest, and the two-particle system has an initial electric potential energy of 0.150 J. Suddenly, the particles are released and fly apart because of the repulsive electric force that acts on each one (see the figure). The effects of the gravitational force are negligible, and no other forces act on the particles. Concepts: (i) What types of energy does the twoparticle system have initially? (ii) What types of energy does the two-particle system have at the instant illustrated in part $b$ of the drawing? (iii) Does the principle of conservation of energy apply to this problem? Explain. (iv) Does the conservation of linear momentum apply to the two particles as they fly apart? Explain. Calculations: At one instant following the release, the speed of particle 1 is measured to be $v_{1}=170 \mathrm{m} / \mathrm{s}$. What is the electric potential energy at this instant?
(a) Two particles have different masses, but the same electrical charge $q$ They are initially at rest.
(b) At the instant following the release of the particles, they are flying apart due to the mutual force of electric
repulsion.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 71

Two identical point charges $\left(+2.4 \times 10^{-9} \mathrm{C}\right)$ are fixed in place, separated by 0.50 $\mathrm{m}$ (see the figure). Concepts: (i) The electric field is a vector and has a direction. At the midpoint, what are the directions of the individual electric-field contributions from $q_{\mathrm{A}}$ and $q_{\mathrm{B}} ?$ (ii) Is the magnitude of the net electric field at the midpoint greater than, less than, or equal to zero? (iii) Is the total electric potential at the midpoint positive, negative, or zero? (iv) Does the electric potential have a direction associated with it? Explain. Calculations: Find the electric field and the electric potential at the midpoint of the line between the charges $q_{\mathrm{A}}$ and $q_{\mathrm{B}}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

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