Deck 23: The Electric Field

Question 1

An electron and proton are separated by $1 \times 10 ^ { - 12 }$ meters. The attractive force between the pair is

A) 2.5 mN.
B) 1.1 mN.
C) 0.23 mN.
D) 0.71 mN.

Answer 1

0.23 mN.

Question 2

Two equal charges are separated by 5 cm; the repulsive force is found to be 2.5 N. The magnitude of one of the charges is

A) $8.3 \times 10 ^ { - 7 } \mathrm { C }$
B) - $7.6 \times 10 ^ { - 13 } \mathrm { C }$
C) $9.4 \times 10 ^ { - 7 } \mathrm { C }$
D) $6.9 \times 10 ^ { - 13 } \mathrm { C }$

Answer 2

$8.3 \times 10 ^ { - 7 } \mathrm { C }$

Question 3

Two electrons are in close proximity; the repulsive force between them is 1.1 $\mu$ N. The distance between the two charges is

A) $3.5 \times 10 ^ { - 11 }$ m.
B) $7.8 \times 10 ^ { - 11 }$ m.
C) $1.4 \times 10 ^ { - 11 }$ m.
D) $5.3 \times 10 ^ { - 11 }$ m.

Answer 3

$1.4 \times 10 ^ { - 11 }$ m.

Question 4

An electron is placed at the origin; it produces an electric field everywhere in space. The electric field at $x = 1$ cm is

A) $+ 14.4 \hat { x }$ $\mu$ N/C.
B) $- 24.1 \hat { y }$ $\mu$ N/C.
C) $+ 24.1 \hat { y }$ $\mu$ N/C.
D) $- 14.4 \hat { x }$ $\mu$ N/C.

Question 5

A 3.4-C charge is embedded in a two-dimensional electric field. At the position of the charge, the electric field is given by $+ 2.3 \hat { x }$ N/C and $- 5.1 \hat { y }$ N/C. The net force acting on the charge is

A) 7.8 N.
B) 17.3 N.
C) 19 N.
D) 25.2 N.

Question 6

A 13.6-N force is acting on an electrical charge. At the location of the charge, the 3.1-N/C electric field points in the opposite direction of the force. The charge is

A) $+ 4.4 \mathrm { C } \text {. }$
B) $- 4.4 \mathrm { C }$
C) $- 230$ mC.
D) $+ 230$ mC.

Question 7

A point charge of $- 3.5$ nC is placed at the origin. The electric field at the location $x = - 0.3$ m, $y = - 0.5$ m is

A) $E = - 47.7 \hat { x } - 79.4 \hat { y }$ N/C.
B) $E = - 47.7 \hat { x } + 79.4 \hat { y }$ N/C.
C) $E = 47.7 \hat { x } - 79.4 \hat { y }$ N/C.
D) $E = 47.7 \hat { x } + 79.4 \hat { y }$ N/C.

Question 8

A point charge of $- 3.5$ nC is placed at the origin. The direction of the electric field at the location $x = - 0.3$ m, $y = - 0.5$ m is (measured counterclockwise from +x)

A) 59º.
B) 239º.
C) 329º.
D) 149º.

Question 9

A charged ring having radius $R$ and total charge $Q$ is lying in the x-y plane and centered at the origin. The expression for the electric field at $z \rightarrow \infty$ (in the z direction) is

A) $E _ { z } = 1 / \left( 4 \pi \varepsilon _ { 0 } \right) Q / z ^ { 2 }$
B) $E _ { z } = 1 / \left( 4 \pi \varepsilon _ { 0 } \right) Q / ( z + R ) ^ { 2 }$
C) $E _ { z } = 1 / \left( 4 \pi \varepsilon _ { 0 } \right) Q / ( z - R ) ^ { 2 }$
D) $E _ { z } = 1 / \left( 4 \pi \varepsilon _ { 0 } \right) Q R / z ^ { 3 }$

Question 10

A charged ring having radius $R$ and total charge $Q$ is lying in the x-y plane and centered at the origin. The expression for the electric field as $z \rightarrow 0$ (in the z direction) is

A) $E _ { z } = 1 / \left( 4 \pi \varepsilon _ { 0 } \right) Q / R ^ { 2 }$
B) $E _ { z } = 1 / \left( 4 \pi \varepsilon _ { 0 } \right) Q / ( z + R ) ^ { 2 }$
C) $E _ { z } = 1 / \left( 4 \pi \varepsilon _ { 0 } \right) Q / ( R - z ) ^ { 2 }$
D) $E _ { z } = 1 / \left( 4 \pi \varepsilon _ { 0 } \right) Q z / R ^ { 3 }$

Question 11

An infinitely long wire has a linear charge density of 1.8 nC/m. The magnitude of the electric field two meters away from the wire is

A) 32 N/C.
B) 64 N/C.
C) 16 N/C.
D) 56 N/C.

Question 12

A wire has a linear charge density $\lambda ( x ) = 2.35 x$ , where $x$ is in meters (m) and $\lambda$ is in C/m. If the length of the wire is 3.7 m, the total charge on the wire is

A) 11 C.
B) 1.2 C.
C) 16 C.
D) 8.0 C.

Question 13

An infinite flat sheet has a surface charge density of $- 15.3$ nC/m $2$ The magnitude of the electric field at a distance of 5.3 cm above the infinite sheet is

A) 620 N/C.
B) 860 N/C.
C) 1200 N/C.
D) 1700 N/C.

Question 14

An infinite flat sheet has a surface charge density of $- 15.3$ nC/m $2$ The direction of the electric field at a distance of 5.3 cm above the infinite sheet

A) is parallel with the surface of the sheet.
B) is perpendicular and pointing away from the sheet.
C) is perpendicular and pointing toward the sheet.
D) cannot be determined.

Question 15

A proton is released from rest in the presence of a static uniform electric field of 18 $\mu$ N/C. The velocity of the proton at four seconds is

A) 8.6 m/s.
B) 1200 m/s.
C) 560 m/s.
D) 6900 m/s.

Question 16

A proton is released from rest in the presence of a static uniform electric field of 18 $\mu$ N/C. The change in the position of the proton at four seconds is

A) 7.8 km.
B) 14 km.
C) 1.3 km.
D) 2.6 km.

Question 17

A dipole of 7.6 $\mu$ C.m is embedded in an external electric field of 3.3 N/C. The angle between the dipole moment and the electric field is 180º. The potential energy of the dipole is

A) $+ 25$ $\mu$ J.
B) 0
C) $- 50$ $\mu$ J.
D) $- 25$ $\mu$ J.

Question 18

The direction of the dipole moment vector is

A) from the negative charge toward the positive charge.
B) given by the right-hand rule.
C) given by the left-hand rule.
D) from the positive charge toward the negative charge.

Question 19

A dipole moment is embedded in an external electric field. The direction of the torque acting on the dipole is

A) from the negative charge towards the positive charge.
B) given by the right-hand rule.
C) given by the left-hand rule.
D) from the positive charge toward the negative charge.

Question 20

A charged particle of mass $10 ^ { - 26 }$ kg is released in a uniform electric field of 1.3 pN/C. The acceleration of the charge is 9100 m/s $2$ Therefore the charge is

A) 70 pC.
B) 18 pC.
C) 3.5 pC.
D) 40 pC.

Question 21

The electric field for an infinite rod of uniform linear charge density goes as

A) $r$
B) $1 / r ^ { 2 }$
C) $r ^ { 2 }$
D) $1 / r$

Question 22

An electric dipole moment is characterized by all of the following except

A) its magnitude is decreased if the magnitude of the charges are decreased.
B) its magnitude is increased if the distance between the charges is increased.
C) its direction is reversed if the two charges are exchanged.
D) its magnitude is decreased as the mass of each charge is decreased.

Question 23

The maximum torque on an electric dipole in a E-field occurs when

A) p is directed along and parallel to E.
B) p is directed opposite and parallel to E.
C) p is directed perpendicular to E.
D) Insufficient information is given to answer.

Question 24

The final (stable) orientation of an electric dipole in a E-field occurs when the torque $\tau$ on the dipole and the potential energy U of the dipole are arranged as follows:

A) $\tau$ is a maximum and U is a minimum.
B) $\tau$ is a minimum and U is zero.
C) $\tau$ is zero and U is a minimum.
D) $\tau$ is zero and U is zero.

Question 25

An electric dipole may experience all of the following except

A) a force in a uniform E-field.
B) a torque in a uniform E-field.
C) a force in a nonuniform E-field.
D) a torque in a nonuniform E-field.

Question 26

So that all of the responses to the previous question would be correct, we would need to "modify" (treat each modification suggested here as independent) the dipole such that

A) one charge would be larger in magnitude than the other.
B) both charges would have the same sign (and magnitude).
C) both charges would be increased in magnitude.
D) the distance between charges would be reduced to zero.

Question 27

If E-field lines are not straight in a certain region of space, in this region

A) charge must exist.
B) the magnitude of E must not be constant.
C) the direction of E must not be constant.
D) Hold it! None of the previous responses is valid.

Question 28

If E-field lines are not parallel in a certain region of space, for this region all of the following statements are valid except

A) charge must exist.
B) the magnitude of E must not be constant.
C) the direction of E must not be constant.
D) a dipole (free to rotate) would experience a force.

Question 29

All of the following statements are true of E-field lines except

A) they start and stop on charges.
B) they cannot exist in a vacuum.
C) they obey the superposition principle.
D) they point in the direction of the force on a positive test charge.

Question 30

E-field lines are correctly described by all of the following except

A) they are more concentrated in regions where the field strength is greater.
B) they are continuous in regions containing no charge.
C) they trace out the path (direction reversed) that would be followed by an electron (with mass) placed in the field and released.
D) they are analogous to streamlines for fluid flow.

Question 31

A time-averaged region of space devoid of particles of matter may nevertheless contain/exhibit/possess all of the following except

A) energy.
B) inertia.
C) angular momentum.
D) charge.

Question 32

The E-field produced by a single point charge Q is characterized by all of the following except

A) it decreases in magnitude with distance from Q.
B) it increases in magnitude as Q increases.
C) it always points radially from (or to) Q.
D) it is modified by other charges in the vicinity of Q.

Question 33

The E-field at point P for each of the following is zero except for the case of

A) any one-dimensional line, P at the geometric center, an identical charge at each end.
B) any one-dimensional line, P located between the two ends of the line, a charge at each end with the same sign and with magnitude equal to the square of its distance from P.
C) any one-dimensional line, P located between the two ends of the line, a charge at each end with magnitude equal to its distance from P.
D) any one-dimensional line, P located beyond one end of the line, a positive charge at one end with magnitude equal to the square of its distance from P, a negative charge at the other end with magnitude equal to the square of its distance from P.

Question 34

The E-field at point P for each of the following is zero except for the case of

A) any two-dimensional regular polygon (such as an equilateral triangle or a square), P at the geometric center, an identical charge at each vertex.
B) any three-dimensional regular solid (such as a cube or a tetrahedron), P at the geometric center, an identical charge at each vertex.
C) any two-dimensional regular polygon with an even number of sides (such as a square or hexagon), P at the geometric center, identical charges (of either sign) at each of a pair of vertices opposite each other.
D) Hold it! There are no exceptions.

Question 35

In a nonuniform E-field, an electric dipole free to rotate and free to translate will be

A) drawn in the direction of the E-field.
B) drawn in a direction opposite to the E-field.
C) drawn in a direction perpendicular to the E-field.
D) Hold it! None of the above answers is correct in general.

Question 36

In a nonuniform E-field, an electric dipole free to rotate and free to translate will be

A) drawn in a direction of stronger E-field.
B) drawn in a direction of weaker E-field.
C) rotated, but not drawn in any direction with respect to the E-field.
D) Hold it! None of the above answers is correct in general.

Question 37

Consider a positively charged square plate of finite size (a few centimeters on edge). Point P' is centered a few centimeters above the plate. If point P' were moved slightly to the left, the direction of the E-field at point P' would (compared to its direction before the movement)

A) remain unchanged.
B) shift slightly toward the top of the plate.
C) shift slightly toward the bottom of the plate.
D) Hold it! None of the above answers is correct.

Question 38

Consider a positively charged square plate of finite size (a few centimeters on edge). Point P' is centered a few centimeters above the plate. If point P' were moved slightly to the left, the direction of the E-field at point P' would (compared to its direction before the movement)

A) shift slightly toward the right of the plate.
B) shift slightly toward the left of the plate.
C) shift slightly out of the plane of the plate.
D) Hold it! None of the above answers is correct.

Question 39

Consider a positively charged square plate of finite size (a few centimeters on edge). Point P' is centered a few centimeters above the plate. As point P' moves perpendicularly away from the plate, the magnitude of the E-field at point P'

A) decreases monotonically (continually) but not uniformly.
B) decreases at first, then increases.
C) does not change.
D) Hold it! None of the above answers is correct.

Question 40

Consider a positively charged square plate of finite size (a few centimeters on edge). Point P' is centered a few centimeters above the plate. As point P' moves perpendicularly away from the plate, the magnitude of the E-field at point P'

A) increases at first, then decreases.
B) increases monotonically (continually) but not uniformly.
C) increases uniformly.
D) Hold it! None of the above answers is correct.

Question 41

Consider a positively charged square plate of finite size (a few centimeters on edge). Point P lies in the same plane as the plate and is a few centimeters away from one edge of the plate. If point P were moved slightly away (perpendicularly) from the plane, the direction of the E-field (compared to its direction before the movement of P) would

A) remain unchanged.
B) shift slightly toward the top of the plate.
C) shift slightly toward the bottom of the plate.
D) Hold it! None of the above answers is correct.

Question 42

Consider a positively charged square plate of finite size (a few centimeters on edge). Point P lies in the same plane as the plate and is a few centimeters away from one edge of the plate. If point P were moved slightly away (parallel with the plane), the magnitude of the E-field (compared to its direction before the movement of P) would

A) increase monotonically (continually) but not uniformly.
B) increase at first, then decrease.
C) decrease monotonically (continually) but not uniformly.
D) decrease at first, then increase.

Question 43

Consider a positively charged wire bent into the shape of a capital "U". Point P is down in the well of the "U" (specifically at the center of curvature). At point P, the direction of the E-field is

A) toward the top of the page.
B) toward the bottom of the page.
C) toward the right of the page.
D) toward the left of the page.

Question 44

Consider a positively charged wire bent into the shape of a capital "U". Point P is down in the well of the "U" (specifically at the center of curvature). If point P were moved slightly toward the top of the page, the direction of the E-field would

A) remain unchanged.
B) shift slightly toward the top of the page.
C) shift slightly toward the bottom of the page.
D) Hold it! None of the above answers is correct.

Question 45

Consider a positively charged wire bent into the shape of a capital "U". Point P is down in the well of the "U" (specifically at the center of curvature). If point P were moved slightly toward the left, the direction of the E-field would

A) shift slightly toward the right of the plate.
B) shift slightly toward the left of the plate.
C) shift slightly out of the plane of the plate.
D) Hold it! None of the above answers is correct.

Question 46

As the location of interest is moved farther away from an infinite plane possessing constant charge per area, the E-field

A) does not change.
B) increases at first, then decreases.
C) decreases at first, then increases.
D) changes monotonically (continually) but not uniformly.

Question 47

Consider a (two-dimensional) ring of positive charge, uniformly distributed. The force on a charge Q placed at a point P located precisely at the geometric center of the ring

A) "repels" (or "attracts") Q from (or to) P along an axial line depending on the sign of Q.
B) "repels" Q from P along a line in the plane of the ring.
C) "attracts" Q to P along a line in the plane of the ring.
D) is precisely zero.

Question 48

Consider a (two-dimensional) ring of positive charge, uniformly distributed. The force on a negative charge Q placed at a point P' located a small distance (in the plane of the ring) from the geometric center of the ring acts as if it

A) "repels" Q from P' along an axial line.
B) "attracts" Q to P' along an axial line.
C) "repels" (or "attracts") Q from (or to) P' along a line in the plane of the ring.
D) is precisely zero.

Question 49

Consider a (two-dimensional) ring of positive charge, uniformly distributed. The force on a negative charge Q placed at a point P* located a small distance (along an axial line, perpendicular to the plane of the ring) from the geometric center of the ring acts as if it

A) "repels" Q from P* along an axial line.
B) "attracts" Q to P* along an axial line.
C) "repels" (or "attracts") Q from (or to) P* along a line in the plane of the ring.
D) is precisely zero.

Question 50

Consider a (two-dimensional) ring of positive charge, uniformly distributed. For a positively charged ring and a point charge Q near its geometric center, Q undergoes one-dimensional SHM for this single conjunction of cases:

A) Q negative: motion in axial direction and motion in plane of ring.
B) Q positive: motion in axial direction and motion in plane of ring.
C) Q negative: motion in axial direction and Q positive, motion in plane of ring.
D) Q positive: motion in axial direction and Q negative, motion in plane of ring.