Deck 29: Magnetic Force and Field

Question 1

The direction of the magnetic field due to a steady current flowing in a straight wire is

A) axial (parallel to the wire).
B) tangent (to a circle around the wire).
C) radial (perpendicular to the wire).
D) none of the above.

Answer 1

tangent (to a circle around the wire).

Question 2

The magnetic force on a charged particle is

A) proportional to the velocity squared of the particle.
B) inversely proportional to the velocity squared of the particle.
C) inversely proportional to the velocity of the particle.
D) proportional to the velocity of the particle.

Answer 2

proportional to the velocity of the particle.

Question 3

The direction of the magnetic force on a charged particle depends on

A) the direction of the magnetic field.
B) the direction of the velocity of the particle.
C) the sign of the particle's charge ( $+ / -$ ).
D) all of the above.

Answer 3

all of the above.

Question 4

At some moment, an electron ( $q = - 1.6 \times 10 ^ { - 19 }$ C) moves with a velocity of 1 m/s orthogonal to a 1-T magnetic field. The force acting on the electron is

A) $0$ N.
B) $1.6 \times 10 ^ { - 19 }$ N.
C) $1.0$ N.
D) $1.0 \times 10 ^ { - 9 }$ N.

Question 5

At some moment, an electron ( $q = - 1.6 \times 10 ^ { - 19 }$ C) moves with a velocity of 1 m/s parallel to a 1-T magnetic field. The force acting on the electron is

A) $0$ N.
B) $1.6 \times 10 ^ { - 19 }$ N.
C) $1.0$ N.
D) $1.0 \times 10 ^ { - 9 }$ N.

Question 6

An electron travels in the $+ \hat { x }$ direction, and the magnetic field points in the $+ \hat { y }$ direction. The direction of the force acting on the electron is

A) $- \hat { x }$
B) $- \hat { Z }$
C) $- \hat { y }$
D) $+ \hat { z }$

Question 7

A proton travels in the $- \hat { x }$ direction, and the magnetic field points in the $+ \hat { y }$ direction. The direction of the force acting on the proton is

A) $- \hat { x }$
B) $- \hat { Z }$
C) $- \hat { y }$
D) $+ \hat { z }$

Question 8

Consider a proton traveling with a velocity v in the presence of both an electric field E and a magnetic field B. If B $\times$ v is exactly equal to E, the Lorentz force (magnitude) acting on the proton is

A) 2 q E.
B) 2 q B v.
C) zero.
D) both (a) and (b) are correct answers.

Question 9

A 2.3-C charge has a velocity of 3.1 cm/s in the presence of a 5.0-T magnetic field. The angle between the velocity vector and the magnetic field vector is 10º. The magnetic force acting on the charge is

A) 0.33 N.
B) 6.2 N.
C) 0.046 N.
D) 62 mN.

Question 10

It's known that over a particular closed Gaussian spherical shell, the upper hemisphere has a net magnetic flux of $- 23.5 \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$ From this, the net magnetic flux of the lower hemisphere must be

A) $- 23.5 \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$
B) $+ 23.5 \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$
C) $0 \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$
D) $- 47.0 \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$

Question 11

The general form of Ampere's Law is

A) $\oint \vec { B } \cdot d \vec { s } = \mu _ { 0 } I$
B) $\oint \vec { B } \cdot d \vec { A } = 0$
C) $\oint \vec { B } \cdot d \vec { s } = 0$
D) $\oint \vec { B } \cdot d \vec { A } = 4 \pi \mu _ { 0 } / r$

Question 12

Consider a long, straight, thin wire carrying a 350-mA steady current. The value of $\oint \vec { B } \cdot d \vec { s }$ computed around the circle of radius 3.1 cm (from the wire) is

A) $1.6 \times 10 ^ { - 8 }$ T.m.
B) $6.5 \times 10 ^ { - 6 }$ T.m.
C) $7.8 \times 10 ^ { - 6 }$ T.m.
D) $4.4 \times 10 ^ { - 7 }$ T.m.

Question 13

Consider a long, straight, thin wire carrying a steady current. The value of $\oint \vec { B } \cdot d \vec { s }$ computed around a circle at some radius (orthogonal from the wire) is

A) larger as the radius is increased.
B) smaller as the radius is increased.
C) constant (not a function of the radius).
D) none of the above.

Question 14

Consider a long, straight, thin wire carrying a steady 0.5-A current. The value of the magnetic field 5 cm from the wire is

A) $4.5 \times 10 ^ { - 6 }$ T.
B) $8.6 \times 10 ^ { - 6 }$ T.
C) $6.5 \times 10 ^ { - 6 }$ T.
D) $2.0 \times 10 ^ { - 6 }$ T.

Question 15

Consider a long, straight, thick wire of radius 1 cm that carries a steady 0.9-A current. The value of the magnetic field 0.5 cm from the center of the wire is

A) $9.0 \times 10 ^ { - 6 }$ T.
B) $1.5 \times 10 ^ { - 6 }$ T.
C) $7.3 \times 10 ^ { - 6 }$ T.
D) $3.0 \times 10 ^ { - 6 }$ T.

Question 16

Consider a long, straight, thick wire of radius 1 cm that carries a steady current. The direction of the magnetic field 0.5 cm from the center of the wire is

A) axial.
B) radial.
C) tangential.
D) none of the above.

Question 17

Consider a thin wire bent into the shape of a ring of radius of 10 cm that carries a steady 2.0-A current. The value of the magnetic field at the center of the ring is

A) $45 \mu$ T.
B) $13 \mu$ T.
C) $25 \mu$ T.
D) $6.3 \mu$ T.

Question 18

A solenoid has a turn ratio of 58 turns per cm and carries a 250-mA current. The magnetic field in the center of the solenoid is

A) 7.6 mT.
B) 6.8 mT.
C) 1.8 mT.
D) 8.6 mT.

Question 19

A solenoid has a turn ratio of 100 turns per cm and carries a steady current. The direction of the magnetic field in the center of the solenoid is

A) axial.
B) tangential.
C) radial.
D) none of the above.

Question 20

A thin wire is bent into a ring, and a steady current flows through the wire. When viewed from overhead (looking downward), the current travels clockwise around the ring. The direction of the magnetic field in the center of the ring is

A) upward.
B) clockwise.
C) downward.
D) counterclockwise.

Question 21

A wire solenoid with 100 total turns is bent into the shape of a torus (doughnut) having a radius $r = 5$ cm. A 730-mA current passes through the wire. The magnetic field inside the torus is

A) 5.6 mT.
B) 13 mT.
C) 0.29 mT.
D) 23 mT.

Question 22

A wire solenoid has 220 loops and a length of 5.5 cm. A 2.3-A current passes through the wire. The magnetic field inside the solenoid is

A) 12 mT.
B) 6.1 mT.
C) 56 mT.
D) 77 mT.

Question 23

In the Biot-Savart Law, the normal of the plane that is formed by the current vector and the r (position) vector is

A) parallel with the magnetic field vector at r.
B) perpendicular to the magnetic field vector at r.
C) skewed to the magnetic field vector at r.
D) both (b) and (c) are correct.

Question 24

A ferromagnetic material is used to

A) enhance (make stronger) the magnetic field in a solenoid.
B) eliminate completely the magnetic field in a solenoid.
C) diminish (make weaker) the magnetic field in a solenoid.
D) enhance the capacitance of a solenoid.

Question 25

Consider a closed Gaussian spherical surface that contains a small bar magnet having four poles (two north and two south). The net flux that passes through the sphere

A) is zero.
B) is infinite.
C) is nonzero but not infinite.
D) is small but not zero.

Question 26

The magnetic force on an electric charge at rest

A) must be zero.
B) may be zero or nonzero.
C) must be nonzero.
D) A magnetic force on an electric charge is a contradiction of terms.

Question 27

The magnetic field produced by an electric charge at rest relative to the observer

A) must be zero.
B) may be zero or nonzero.
C) must be nonzero.
D) A magnetic field cannot be produced by an electric charge.

Question 28

The direction of the force on an electric charge moving in a magnetic field is perpendicular to the

A) velocity of the charge.
B) direction of the magnetic field.
C) Both of the previous responses are valid.
D) The force is parallel to both quantities listed in the first two responses.

Question 29

Gauss' Law for magnetism is

A) $\oint \overrightarrow { \mathrm { B } } \cdot \mathrm { d } \overrightarrow { \mathrm { S } }$ = 0, only if no magnets are inside the surface.
B) $\oint \overrightarrow { \mathrm { B } } \cdot \mathrm { d } \overrightarrow { \mathrm { l } }$ = 0, only if no magnets are inside the loop.
C) $\oint \overrightarrow { \mathrm { B } } \cdot \mathrm { d } \overrightarrow { \mathrm { S } }$ = 0.
D) $\oint \overrightarrow { \mathrm { B } } \cdot \mathrm { d } \overrightarrow { \mathrm { l } }$ = 0.

Question 30

The Law of Biot-Savart is

A) $\mathrm { d } \mathbf { B } = - \left( \mu _ { 0 } / 4 \pi \right) I \mathrm {~d} \mathbf { l } \times \mathbf { r } ^ { 2 }$
B) $\mathrm { d } \mathbf { B } = - \left( \mu _ { 0 } / 4 \pi \right) I \mathrm {~d} \mathbf { l } \times \mathbf { r }$
C) $\mathrm { d } \mathbf { B } = \left( \mu _ { 0 } / 4 \pi \right) I \mathrm {~d} \mathbf { l } \times \mathbf { r } ^ { 3 }$
D) $\mathrm { d } \mathbf { B } = \left( \mu _ { 0 } / 4 \pi \right) I \mathrm {~d} \mathbf { l } \times \mathbf { r } ^ { 2 }$

Question 31

The symbol $\mu _ { 0 }$ has the same units as

A) $\mu$ , the magnetic dipole moment.
B) $\varepsilon _ { 0 }$ , the permittivity constant.
C) G, the universal gravitational constant.
D) none of the above.

Question 32

The magnetic force between a moving charge and a second charge is always zero if the second charge

A) is at rest.
B) moves along the line joining the two charges.
C) Both of the first two responses are valid.
D) Neither of the first two responses is valid.

Question 33

The magnitude of the magnetic field of a magnetic dipole as a function of the distance r (along the dipole axis) is proportional to

A) 1/r.
B) 1/r².
C) 1/r³.
D) 1/r⁴.

Question 34

The magnitude of the magnetic field of a straight (infinitely long) current-bearing wire as a function of the distance r (from the wire) is proportional to

A) 1/r.
B) 1/r².
C) 1/r³.
D) 1/r⁴.

Question 35

The magnitude of the magnetic field of a circular loop of current-bearing wire at the geometric center of a loop of radius r is proportional to

A) 1/r.
B) 1/r².
C) 1/r³.
D) 1/r⁴.

Question 36

The dimensions of $\mu _ { 0 }$ are

A) [newtons] [meters]/ [coulombs].
B) [newtons] [meters]/ [coulombs]².
C) [newtons] [seconds]²/ [coulombs]².
D) [newtons] [meters/second]²/ [coulombs]².

Question 37

All of the following are acceptable units for magnetic fields except

A) gauss.
B) tesla.
C) weber/meter².
D) There are no exceptions.

Question 38

An electron travels along a straight path from left to right in a plane parallel to and directly below your test paper. The consequent magnetic field (due to the electron's motion) at a point on your test paper directly above the electron path is in the direction

A) out of the paper, toward the reader.
B) into the paper, away from the reader.
C) toward the top of the paper, in its plane.
D) toward the bottom of the paper, in its plane.

Question 39

A second electron (see the previous question) travels along a straight path (in step with the first electron) from left to right in the plane of your test paper. The consequent electrical force on the second electron at a point on your test paper is in the direction

A) out of the paper, toward the reader.
B) into the paper, away from the reader.
C) toward the top of the paper, in its plane.
D) toward the bottom of the paper, in its plane.

Question 40

A second electron (see question 39) travels along a straight path (in step with the first electron) from left to right in a plane parallel to and in the plane of your test paper. The consequent magnetic force on the second electron at a point on your test paper is in the direction

A) out of the paper, toward the reader.
B) into the paper, away from the reader.
C) toward the top of the paper, in its plane.
D) toward the bottom of the paper, in its plane.

Question 41

Consider the magnetic field created by a loop of current-bearing wire along a line on the axis of the loop. At the geometric center of a circular loop, the magnitude of the magnetic field goes through a

A) maximum.
B) minimum.
C) point of inflection.
D) None of the previous answers is correct.

Question 42

For magnetic forces, there are circumstances under which

A) Newton's Third Law fails, despite accounting for field effects.
B) the law of conservation of momentum fails, despite accounting for field effects.
C) Both of the first two responses are valid.
D) Neither of the first two responses is valid.

Question 43

For magnetic forces under the circumstance of steady currents flowing in closed circuits, it is still possible that

A) Newton's Third Law fails.
B) the law of the conservation of momentum fails.
C) Both of the first two responses are valid.
D) Neither of the first two responses is valid.

Question 44

The correct relationship of the magnitudes of the magnetic force F_m between two electrons to the electric force F_e between the same two electrons is always

A) F_m > F_e.
B) F_m = F_e.
C) F_m < F_e.
D) Hold it! There are no such restrictions.

Question 45

The formula for the magnetic field at a distance z along the axis of a loop of a current-bearing wire with loop radius R is the same as that for a magnetic dipole, provided

A) z >> R.
B) z = R.
C) z << R.
D) Hold it! More than one of the previous responses is valid.

Question 46

All of the following "natural" bodies possess magnetic dipole moments except

A) electrons.
B) protons.
C) the Earth.
D) There are no exceptions.

Question 47

All of the following charge-movement configurations would produce a magnetic dipole moment except

A) charge flowing in a circle.
B) charge flowing radially outward (with spherical symmetry) from a central point.
C) charge flowing along the perimeter of a "loop" with square corners.
D) Hold it! There are no exceptions.

Question 48

The magnetic field at the midpoint between two parallel (straight) current-bearing wires (current traveling in same direction) is (using the right-hand rule)

A) double what it would be due to a single wire.
B) equal to what it would be due to a single wire.
C) half what it would be due to a single wire.
D) exactly zero.

Question 49

The magnetic field at a distance r from one current-bearing wire, with a second identical wire the same distance r on the opposite side of the first wire, is (using the superposition principle)

A) double what it would be due to a single wire.
B) three-halves what it would be due to a single wire.
C) five-fourths what it would be due to a single wire.
D) half what it would be due to a single wire.