Deck 25: Electrostatic Potential and Energy

Question 1

All of the following are legitimate units for electric field except

A) [newton]/[coulomb].
B) [volt]/[meter].
C) [electron-volt].
D) There are no exceptions; all of the above are legitimate units.

Answer 1

[electron-volt].

Question 2

All of the following are legitimate units for the electric potential except

A) [newton][meter]/[coulomb]. .
B) [volt].
C) [electron-volt].
D) There are no exceptions; all of the above are legitimate units.

Answer 2

[electron-volt].

Question 3

The difference in electric potential between the accelerating plates in the electron gun of a TV tube is 25 kV, while the distance between them is 1.5 cm. The magnitude of the uniform electric field between the plates is

A) 1.7 * 10⁶ v/m.
B) 3.8* 10² v/m.
C) 11*10⁸ v/m.
D) 5.6 *10² v/m.

Answer 3

3.8* 10² v/m.

Question 4

The electric field in a region is nonzero. The statement that most precisely describes the electric potential in that region is

A) the electric potential must vary in the region.
B) the electric potential has a maximum somewhere in that region.
C) the electric potential has a minimum somewhere in that region.
D) the electric potential is uniform throughout the region.

Question 5

Inside a perfect conductor

A) the electric field is zero throughout, even at the surfaces.
B) the electric field is constant throughout, even at the surfaces.
C) the electric potential is zero throughout, even at the surfaces.
D) the electric potential is constant throughout, even at the surfaces.
E) none of the above is correct.

Question 6

A Na⁺/K⁺ pump is found in the membranes of many types of cells. Three Na⁺ ions are pumped out of the cell for every two K⁺ ions pumped into the cell. As a result, positive charge builds up outside the cell compared to inside the cell. The potential difference across the membranes allows neurons to generate electrical impulses that lead to nerve impulses. The direction of the electric field produced

A) is tangent to the neuron's surface.
B) points from inside toward outside.
C) points from outside toward inside.
D) There is no electric field.

Question 7

A ring of radius a, made of a nonconducting material, holds a positive charge +q on its bottom half and a negative charge -q on its top half. The electric potential at the center of the ring is

A) -kq/2a.
B) kq/2a.
C) 0 V.
D) kq/a.
E) -kq/a.

Question 8

A spherical balloon contains a positively charged particle at its center. As the balloon is inflated to a greater volume while maintaining the charged object at the center,

A) the electric potential at the surface of the balloon increases while the electric flux through the balloon's surface decreases.
B) the electric potential at the surface of the balloon increases while the electric flux through the balloon's surface increases.
C) the electric potential at the surface of the balloon decreases while the electric flux through the balloon's surface decreases.
D) the electric potential at the surface of the balloon decreases while the electric flux through the balloon's surface increases.
E) none of the above is correct.

Question 9

If the electrostatic potential at a point P is negative, then

A) bringing a positive charge +q from infinity to P would require positive work to be done on +q by an external force.
B) bringing a negative charge -q from infinity to P would require positive work to be done on -q by an external force.
C) bringing a negative charge -q from infinity to P would require negative work to be done on -q by an external force.
D) there is an electric field at P.
E) none of the previous answers is correct.

Question 10

The electric potential at a distance of 2.0 * 10^-10 m from a nucleus of charge +12e is

A) 27 V.
B) 43 V.
C) 54 V.
D) 86 V.
E) 140 V.

Question 11

The electric potential at the center of a square of side 40 cm is 4.0 V when a charge +Q is located at one of the square's corners. When a charge -Q is placed at the opposite corner, the electric potential at the square's center is

A) 0.0 V.
B) 2.0 V.
C) 4.0 V.
D) 8.0 V.

Question 12

Rank the following situations based on the electric potential at point (0 cm, 0 cm):

A) V_B < V_A = V_C < V_D.
B) V_D > V_A = V_B =V_C.
C) V_A = V_B = V_C = V_D.
D) V_A = V_B = V_C > V_D.
E) V_D < V_A = V_B =V_C.

Question 13

A charge +Q is placed on a solid spherical conductor. The electrostatic potential of the sphere is

A) constant throughout the whole volume of the sphere.
B) the largest at the center of the sphere.
C) the largest somewhere between the center and the surface.
D) the largest at the surface of the sphere.

Question 14

A uniform electric field of 10 N/C points in the direction of the positive x axis. If the electric potential at x = 4.0 m is 80 V, the electric potential at x = -2.0 m is

A) -20 V.
B) 20 V.
C) 60 V.
D) 100 V
E) 140 V.

Question 15

As the distance from a negatively charged sheet of infinite dimensions and uniform charge density increases, the electric potential

A) decreases.
B) does not change.
C) increases.
D) is unknown; more information is needed to work out the answer.

Question 16

A charge +q₁ is brought to a point a distance r from a charge +q. Then +q₁ is removed and a charge -q₁ is brought to the same point. If in the first case the electrostatic potential at r is V, the electrostatic potential at the same point in the second case is

A) -2V.
B) -V.
C) 0.
D)V.
E) 2V.

Question 17

A charge +q₁ is brought to a point a distance r₁ from a charge +q. Then +q₁ is removed and a charge +4q₁ is brought to a point a distance 2r₁ from +q. If the electrostatic potential at r₁ is V, the electrostatic potential at 2r₁ is

A) V/4.
B) V/2.
C) V.
D) 2V.
E) 4V.

Question 18

Two conducting spheres are made of the same material and have radii r and 2r. The spheres are placed a distance d > 2r from each other and have initial charges of -2Q and -4Q respectively. The point on the line connecting the centers of the two spherical shells where the electric potential is zero is

A) closer to -2Q.
B) closer to -4Q.
C) mid-distance between -2Q and -4Q.
D) There is no point on the line connecting the centers of the two spherical shells where the electric potential is zero.
E) More information is needed to work out the answer.

Question 19

Two conducting spherical shells, A and B, are made of the same material, have radii r and 2r, and have initial charges of -Q. When sphere A is brought into a space free of other charges, the electric potential at a distance R > 2r from the center of the sphere is -V. Sphere A is removed, and sphere B is brought to the same point. The electric potential due to sphere B at a distance R from its center is

A) 2V.
B) V.
C) 0 V.
D) -V.
E) -2V.

Question 20

Two conducting spheres, A and B, are made of the same material and have radii r and 2r. The spheres are placed a distance d > 3r from each other. The first sphere has an initial charge Q, while the second is uncharged. The spheres are initially connected by a thin conducting wire; the wire is then removed. When electrostatic equilibrium has been reached, the electrostatic potentials of the two spheres are related by

A) V_A > V_B.
B) V_A = V_B.
C) V_A < V_B.
D) More information is needed to work out the answer.

Question 21

Two identical conducting spheres are placed a distance d from each other and have initial charges of -2Q and 8Q, respectively. The spheres are initially connected by a thin conducting wire; the wire is then removed. The charges on the spheres after the removal of the wire are

A) -2Q and 8Q.
B) 0 and 6Q.
C) 3Q and 3Q.
D) 6Q and 0.
E) 8Q and -2Q.

Question 22

Two conducting spheres are made of the same material and have radii r and 2r. The spheres are placed a distance d > 3r from each other and have initial charges of -2Q and 8Q, respectively. The spheres are initially connected by a thin conducting wire; the wire is then removed. The charges on the spheres after the removal of the wire are

A) -2Q and 8Q.
B) 2Q and 4Q.
C) 3Q and 3Q.
D) 4Q and 2Q.
E) 8Q and -2Q.

Question 23

Two conducting spheres, A and B, are made of the same material and have radii r and 2r. The spheres are placed a distance d > 3r from each other. The first sphere has an initial charge Q, while the second is uncharged. The spheres are initially connected by a thin conducting wire; the wire is then removed. When electrostatic equilibrium has been reached, the magnitudes of the electric fields near the surfaces of the respective spheres are related by

A) E_A > E_B.
B) E_A = E_B.
C) E_A < E_B.
D) More information is needed to work out the answer.

Question 24

The electric potential of a spherical shell of radius R and charge Q at any point outside the shell a distance r from the center is proportional to

A) Q / r.
B) Q / R.
C) Q / (r + R).
D) Q / (r - R).
E) Q (r + R) / rR.

Question 25

The electric potential of a spherical shell of radius R and charge Q at any point inside the shell a distance r from the center is proportional to

A) Q / r.
B) Q / R.
C) Q / (r + R).
D) Q / (r - R).
E) Q (r + R) / rR.

Question 26

Two concentric conducting spherical shells have radii r and R (> r) and charges q and Q, respectively. The electric potential just outside the surface of the shell of smaller radius is proportional to

A) q / r + Q / R.
B) q / R + Q / r.
C) q / r + (q + Q) / (r + R).
D) q / R + (q + Q) / r.
E) q / r + (q + Q) / R.

Question 27

Two concentric conducting spherical shells have radii r and R (> r) and charges q and Q, respectively. It can be shown that the electric potential difference between the two shells, V_R - V_r, is proportional to q(1/R - 1/r). If a thin conducting string connects the two shells, charge

A) would flow from the smaller to the larger sphere.
B) would flow from the larger to the smaller sphere.
C) would flow from the smaller to the larger sphere or from the larger to the smaller sphere depending on the signs of the charges on the spheres.
D) would not flow between the spheres at all.
E) More information is needed to work out the answer.

Question 28

The electric potential due to a dipole at a point situated at a distance r, larger than the distance between the dipole's charges, varies as

A) 1 / r³.
B) 1 / r².
C) 1 / r.
D) 1 / r^1/3.
E) none of the above.

Question 29

The electric potential due to a dipole at a point situated at a distance d, larger than the distance between the dipole's charges, is larger when

A) the point is closer to the positive charge than to the negative charge.
B) the point is located symmetrically between the positive and negative charges.
C) the point is closer to the negative charge than to the positive charge.
D) All of the previous responses are correct because the electric potential is constant all around the dipole.
E) None of the previous responses is correct.

Question 30

The electric potential in a certain region in space is given by $V ( x , y , z ) = x ^ { 2 } - y z$ V. The electric field at the point (1.0 m, 0 m, -1.0 m) is

A) 2i + j N/m.
B) -2i - j N/m.
C) 2i N/m.
D) -2i N/m.
E) -2i - k N/m.

Question 31

For an equipotential surface, all of the following are valid except

A) the electric field must intersect it perpendicularly.
B) a charge moving on the surface does no work.
C) an equipotential surface never intersects another equipotential surface.
D) All of the above are true.
E) None of the above is true.

Question 32

The figure here shows the equipotential lines in a certain region in the x-y plane. The vector that best represents the electric field at the point on the 50-V equipotential line where the vectors have been drawn is

A) A
B) B
C) C
D) D

Question 33

As we move along the axis of a ring of uniform charge distribution from infinity to the geometric center, the electric field reaches a maximum in magnitude. The electric potential reaches

A) a maximum at that same point.
B) a minimum at that same point.
C) a maximum at a different point.
D) a minimum at a point some finite distance from the ring.
E) neither a maximum nor a minimum-it is constant.

Question 34

The figure here shows the equipotential lines in a certain region in the x-y plane. The electric field at point (1.0 cm, 4.0 cm) has

A) a positive x component and a negative y component.
B) a negative x component and a negative y component.
C) a positive x component and no y component.
D) a negative x component and a positive y component.
E) a positive x component and a positive y component.

Question 35

The figure here shows the equipotential lines in a certain region in the x-y plane. The electric field at point (3.0 cm, 3.5 cm) is

A) 250i N/C.
B) 250j N/C.
C) 500i N/C.
D) 500j N/C.
E) -500j N/C.

Question 36

The figure here shows a graph of the electric potential (independent of y and z) versus x in a certain region of space. The x component of the corresponding electric field at x = -2.0 cm is

A) 3.0 N/C.
B) -3.0 N/C.
C) undefined.
D) -1.0 N/C.
E) 1.0 N/C.

Question 37

The figure here shows a graph of the electric potential (independent of y and z) versus x in a certain region of space. The graph of the x component of the corresponding electric field versus x is

A) A
B) B
C) C
D) D

Question 38

A charged particle is moved a distance d in a uniform electric field E, as shown in the figure here. The displacement vector makes an angle $$\alpha$$ with the direction of the electric field. The change in the electric potential experienced by the particle is

A) Ed cos $\alpha$
B) Ed sin $\alpha$
C) Ed.
D) (E sin $\alpha$ )|d
E) (E cos $\alpha$ )|d

Question 39

Work is done on a charged particle to move it a distance d in a uniform electric field E, as shown in the figure here. The particle is

A) positively charged.
B) electrically neutral.
C) negatively charged.

Question 40

A charge q is moved a distance d in a uniform electric field E, as shown in the figure here. The displacement vector makes an angle $\alpha$ with the direction of the electric field. The work done on the charge is

A) - qEd cos $\alpha$
B) - qEd sin $\alpha$
C) qEd.
D) qEd sin $\alpha$
E) qEd cos $\alpha$

Question 41

Four charges are moved in a uniform electric field E on the paths shown in the figure here. The dots represent the initial and the arrows the final positions of the charges. The same amount of work was done on charges

A) 1 and 2.
B) 3 and 4.
C) 2, 3, and 4.
D) 1, 2, 3, and 4.
E) A different amount of work was done on each of the charges.

Question 42

Four negative charges are moving in a uniform electric field E on the paths shown in the figure here. The dots represent the initial and the arrows the final positions of the charges. The charges experiencing a change in their electric potential energy are

A) 1 and 2.
B) 3 and 4.
C) 2, 3, and 4.
D) 1, 2, 3, and 4.

Question 43

Four negative charges are moved in a uniform electric field E on the paths shown in the figure here. The dots represent the initial and the arrows the final positions of the charge. The charges that increased their electric potential energy are

A) 1 and 2.
B) 3 and 4.
C) 2, 3, and 4.
D) 1, 2, 3, and 4.

Question 44

A charge +q₁ is brought to a point a distance r₁ from a charge +q. Then +q₁ is removed and a charge +4q₁ is brought to a point a distance 2r₁ from +q. The electrostatic potential energy is

A) smaller for +q₁.
B) smaller for +4q₁.
C) the same for both +q₁ and +4q₁.
D) unknown; more information is needed to work out the answer.

Question 45

A charge +q₁ is brought to a point a distance r from a charge +q. Then +q₁ is removed and a charge -q₁ is brought to the same point. The electrostatic potential energy is

A) smaller for +q₁.
B) smaller for -q₁.
C) the same for both +q₁ and -q₁.
D) unknown; more information is needed to work out the answer.

Question 46

When moving a distance d in a uniform electric field, a proton acquires 5.0 V of electric potential. If three protons are moving the same distance in the same uniform electric field, the electric potential each of them acquires is

A) 0 V.
B) 5/3 V.
C) 3.0 V.
D) 5.0 V.
E) 15 V.

Question 47

The work done to assemble four identical -3.0 nC charges at the corners of a square of side 4.0 cm is

A) 1.1*10^-7 J.
B) -1.1 * 10^-7 J.
C) 1.1 * 10^-5 J.
D) -1.1 * 10^-5 J.
E) 4.4 * 10^-7 J.

Question 48

A -1.0 nC charge is moved from (2.0 cm, 2.0 cm) to (-2.0 cm, -1.0 cm) in the electrostatic field created by the two charges in the figure here. The work done on the -1.0 nC charge is

A) 1.5 * 10^-7 J.
B) 1.5 * 10^-9 J.
C) -1.5*10^-7 J.
D) -1.5 *10^-9 J.
E) 32 *10^-7 J.

Question 49

A -1.0 nC charge is moved from (2.0 cm, 2.0 cm) to (-2.0 cm, -1.0 cm) in the electrostatic field created by the two charges in the figure here. The change in the potential energy of the three-charge system is

A) 1.5 *10^-7 J.
B) 1.5 * 10^-9 J.
C) -1.5 * 10^-7 J.
D) -1.5 * 10^-9 J.
E) 32 * 10^-7 J.

Question 50

The Bohr model for the hydrogen atom states that a single electron can exist only in the orbits whose radii are r = (0.0529)n² nm, where n is a positive integer number. The electric potential energy of a hydrogen atom in which the electron in the third allowed orbit (n = 3) measured in eV (1 eV = 1.6 * 10^-19 J) is

A) 3.0 eV.
B) -3.0 eV.
C) 6.0 eV.
D) -3.0 * 10^-9 eV.
E) 3.0 * 10^-9 eV.

Question 51

Four small spheres, each of mass m, connected by four nonconducting strings to form a square with side d, are placed on a horizontal, nonconducting, frictionless surface. Balls A and B, placed on adjacent corners, each have a charge Q; balls C and D are uncharged. The maximum speed of balls C and D after the string connecting balls A and B is cut is

A) 2(kQ²/3md)².
B) (2kQ²/3md)².
C) (4kQ²/9md²)^1/2.
D) (2kQ²/3md)^1/2.
E) 2(kQ²/3md)^1/2.

Question 52

A uranium nucleus fissions in two spherical fragments of charge 38e and 54e and radii 5.5 * 10^-15 m and 6.2 *10^-15 m, respectively. Assume that the charge is distributed uniformly throughout the volumes, that just before separation each fragment is at rest, and that fragments surfaces are in contact. The electric potential energy of two spherical fragments in MeV (1 MeV = 1.6 *10^-13 J) is

A) 250 MeV.
B) 220 MeV.
C) 80 MeV.
D) 15 MeV.
E) 1.0 MeV.