Deck 30: Charges and Currents in Magnetic Fields

Question 1

A particle with a charge of 1.60 $\times$ 10^-19 and a mass of 1.67 $\times$ 10^-27 kg is found moving in a uniform magnetic field of a strength 1.50 T. The trajectory of the particle is perpendicular to the magnetic field and is circular with a radius of 1.80 cm. The velocity of the particle is

A) 2.6 $\times$ 10⁶ m/s.
B) 2.6 $\times$ 10³ m/s.
C) 2.6 $\times$ 10⁴ m/s.
D) greater than 4.0 $\times$ 10⁶ m/s.

Answer 1

2.6 $\times$ 10⁶ m/s.

Question 2

A particle with a charge of 1.60 $\times$ 10^-19 and a mass of 1.67 $\times$ 10^-27 kg is found moving in a uniform magnetic field of a strength 1.50 T. The trajectory of the particle is perpendicular to the magnetic field and is circular with a radius of 1.80 cm. The kinetic energy of the particle is

A) 13.7 keV.
B) 27.5 keV.
C) 35.0 keV.
D) 45.5 keV.

Answer 2

27.5 keV.

Question 3

A particle with a charge of 1.60 $\times$ 10^-19 and a mass of 1.67 $\times$ 10^-27 kg is found moving in a uniform magnetic field of a strength 1.50 T. The trajectory of the particle is perpendicular to the magnetic field and is circular with a radius of 1.80 cm. The cyclotron frequency is

A) 14 MHz.
B) 23 MHz.
C) 27 MHz.
D) 27 Hz.

Answer 3

23 MHz.

Question 4

The cyclotron frequency depends on the following parameters except

A) charge.
B) magnetic field.
C) mass.
D) velocity.
E) Hold on; the cyclotron frequency depends on all of the above parameters.

Question 5

Two electrons are moving in a uniform magnetic field. The velocity of the first electron is twice the velocity of the second electron. The electron that has the larger circular radius is

A) the first electron.
B) the second electron.
C) Both trajectories have the same radius.
D) The paths of these electrons are not circular.

Question 6

Two electrons are moving in a uniform magnetic field. The velocity of the first electron is twice the velocity of the second electron. The electron that has the longer period of motion around the cyclotron is

A) the first electron.
B) the second electron.
C) Both trajectories have the same period.
D) The paths of these electrons are not circular.

Question 7

The current in a wire is directed along the x axis in a uniform magnetic field that is directed along the negative x axis. The force on the wire is along the

A) x axis.
B) -y axis.
C) z axis.
D) There is no force on the wire.

Question 8

A 25-cm length of wire that is carrying a current of 4.0 A is parallel to a uniform magnetic field of 2.5 T. The force on the wire is

A) 2.5 N.
B) 0.40 N.
C) 5.0 N.
D) zero.

Question 9

The current in a wire is directed along the y axis in a uniform magnetic field that is directed along the negative x axis. The force on the wire is along the

A) z axis.
B) -z axis.
C) +x axis.
D) Hold on. There is no force on the wire.

Question 10

The current in a wire is directed along the y axis in a uniform magnetic field. The resulting force on the wire is directed along the negative x axis. The magnetic field is directed along the

A) z axis.
B) -z axis.
C) +x axis.
D) -y axis.

Question 11

A 20.0-cm length of wire is aligned along the x axis and carries 5.0 mA of current. The wire is in a region where the uniform magnetic field is given by 1.5(i + 2j) mT. The net force on the wire is

A) 1.5 $\mu$ N.
B) 3.0 $\mu$ N.
C) 4.5 $\mu$ N.
D) 7.5 $\mu$ N.

Question 12

A 20.0-cm length of wire is aligned along the x axis and carries 5.0 mA of current. The wire is in a region where the uniform magnetic field is given by 1.5(i + 3j + 4k) mT. The net force on the wire is

A) 1.5 $\mu$ N.
B) 3.0 $\mu$ N.
C) 4.5 $\mu$ N.
D) 7.5 $\mu$ N.

Question 13

A wire carries 5.00 mA of current in a region where the uniform magnetic field strength is 1.50 mT. If the angle between the wire and the magnetic field is 30°, the net force per unit length on the wire is

A) zero.
B) 3.75 $\mu$ N/m.
C) 6.50 $\mu$ N/m.
D) 7.50 $\mu$ N/m.

Question 14

A wire carries 5.00 mA of current in a region where the uniform magnetic field strength is 1.50 mT. If the net force per unit length on the wire is 4.5 $\mu$ N/m, the angle between the current and the magnetic field is

A) zero.
B) 31°.
C) 37°.
D) 53°.

Question 15

Two parallel wires separated by 1.5 cm both carry 1.5 A of current. The magnitude of the force per unit length on one of the wires is

A) 7.5 $\mu$ N/m.
B) 15 $\mu$ N/m.
C) 20 $\mu$ N/m.
D) 30. $\mu$ N/m.

Question 16

A force per unit length of 48 $\mu$ N/m is produced when two wires separated by 1.5 mm both carry the same current. The current the wires carry is

A) 0.36 A.
B) 0.60 A.
C) 0.77 A.
D) 1.0 A.

Question 17

The force produced by two parallel wires with currents running in the same direction will be

A) attractive.
B) repulsive.
C) along the axis of symmetry.
D) zero.

Question 18

A repulsive force is produced between two parallel wires. The relative directions of the currents in the wires

A) are in the same direction.
B) are in the opposite direction.
C) cannot be determined from the information given.
D) depend on the charge carriers in the wires.

Question 19

Two current-carrying wires produce a repulsive force of magnitude F₀. The current in each wire is doubled, resulting in a force whose magnitude is

A) (1/2)F₀.
B) F₀.
C) 2F₀.
D) 4F₀.

Question 20

Two current-carrying wires produce a repulsive force of magnitude F₀ when the wires are separated by a distance of r₀. The distance between the two wires is changed to 2r₀, resulting in a force whose magnitude is

A) (1/2)F₀.
B) F₀.
C) 2F₀.
D) 4F₀.

Question 21

Two current-carrying wires produce a repulsive force of magnitude F₀ when the wires are separated by a distance of r₀. If the current is doubled in each wire while the distance between the two wires is changed to 2r₀, a force results with a magnitude of

A) (1/2)F₀.
B) F₀.
C) 2F₀.
D) 4F₀.

Question 22

The SI unit associate with the magnetic moment $\mu$ , is

A) ampere·m².
B) ampere/m².
C) ampere²·m.
D) ampere²/m².

Question 23

A loop of wire has an area of 0.10 m² and carries 15 mA of current. The magnetic moment of the loop is

A) 0.001 A·m².
B) 0.15 A/m².
C) 71 *10^-5 A²/m.
D) 2.25 A²/m².

Question 24

The maximum torque of a 100-turn loop of wire that has an area of 0.15 m² and is carrying 1.5 A of current in a uniform magnetic field of 2.0 T is

A) zero.
B) 5.0 N·m.
C) 15 N·m.
D) 45 N·m.

Question 25

A 100-turn loop of wire whose area is 0.15 m² carries 3.0 A of current. If a uniform magnetic field of 2.0 T makes an angle of 60° with the plane of the loop, the maximum torque on the loop is

A) zero.
B) 5.0 N·m.
C) 15 N·m.
D) 45 N·m.

Question 26

A rectangular loop of wire whose dimensions are 15 cm * 25 cm carries a current of 5.0 A. The loop is in a uniform magnetic field of 1.5 T whose direction is parallel to the plane of the loop. The torque acting on the loop is

A) zero.
B) 0.24 N·m.
C) 0.28 N·m.
D) 0.35 N·m.

Question 27

A rectangular loop of wire whose dimensions are 15 cm * 25 cm carries a current of 5.0 A. The loop is in a uniform magnetic field of 1.5 T whose direction is perpendicular to the plane of the loop. The torque acting on the loop is

A) zero.
B) 0.24 N·m.
C) 0.28 N·m.
D) 0.35 N·m.

Question 28

The magnitude of the torque produced by a magnetic moment $\mu$ = 2.0 (2i + j) A·m² in a magnetic field given by 1.5 (i + 4k) mT is

A) zero.
B) 3 mN·m.
C) 9 mN·m.
D) 27 mN·m.

Question 29

The magnitude of the torque produced by a magnetic moment $\mu$ = 2.0 (2i + j) A·m² in a magnetic field given by 1.5 (i + k) mT is

A) 3.0 (i - 2j - 2k) mN·m.
B) 9.0 mN·m.
C) 3(-i + 2j - 2k) mN·m.
D) zero.

Question 30

The potential energy of a magnetic moment $\mu$ = 1.0 (2i + j) A·m² in a magnetic field given by 1.5 (2i + k) mT is

A) -6.0 mJ.
B) -3.0 mJ.
C) 3.0 mJ.
D) -1.5 mJ.

Question 31

The potential energy of a magnetic moment $\mu$ = 1.0 (-2i + j + k) A·m² in a magnetic field given by 1.5 (i + j + k)mT is

A) zero.
B) -3.0 mJ.
C) 3.0 mJ.
D) -1.5 mJ.

Question 32

The maximum energy difference between the parallel and antiparallel configurations produced by a magnetic moment whose magnitude is $\mu$ = 2.0 A·m² in a magnetic field given by 1.5 mT is

A) zero.
B) 1.5 mJ.
C) 3.0 mJ.
D) 6.0 mJ.

Question 33

The SI units associated with magnetic susceptibility are

A) A/m².
B) T/m².
C) T·m.
D) Hold on; the magnetic susceptibility is dimensionless.

Question 34

Materials with a small positive magnetic susceptibility are called

A) paramagnets.
B) diamagnets.
C) ferromagnets.
D) permanent magnets.

Question 35

Materials with a small negative magnetic susceptibility are called

A) paramagnets.
B) diamagnets.
C) ferromagnets.
D) permanent magnets.

Question 36

The SI units associated with magnetic permeability are

A) N·s/C.
B) N·s²/C.
C) N·s²/C².
D) Hold on; the magnetic permeability is dimensionless.

Question 37

For a magnetic material the ratio of the magnetic permeability to the permeability of free space is 3. The ratio of the B_matter/B_external for this material is

A) zero.
B) 2
C) 3
D) 4

Question 38

For a magnetic material the ratio of the magnetic permeability to the permeability of free space is 11. The material is placed in a uniform magnetic field of strength 1.0 mT. The magnetic field produced in the material is approximately

A) 11 mT.
B) 10 mT.
C) 1.2 mT.
D) 1.0 mT.

Question 39

A Hall voltage is measured across the width of two rods under the same experimental conditions. The only variation is that the width of the second rod is twice that of the first rod. The Hall voltage across the second rod will be

A) twice the value measured across the first rod.
B) half of the value measured across the first rod.
C) one-quarter the value measured across the first rod.
D) Hold on; the value of the voltage will not change.

Question 40

A Hall voltage is measured across the width of two rods under the same experimental conditions. The only variation is that the thickness of the second rod is twice that of the first rod. The Hall voltage across the second rod will be

A) twice the value measured across the first rod.
B) half of the value measured across the first rod.
C) one-quarter the value measured across the first rod.
D) Hold on; the value of the voltage will not change.

Question 41

A Hall voltage is measured to be 15 $\mu$ V across the 3.0-mm dimension of a slab of copper whose overall dimensions are 2.0 * 3.0 *25.4 mm. The current passing through the copper is 20.0 A, while the magnetic field is 0.010 T. The density of the charge carriers in the material is

A) 3.3 *10²⁴ m^-3.
B) 2.8 *10²⁵ m^-3.
C) 4.2* 10²⁵ m^-3.

Question 42

A Hall voltage of 15 $\mu$ V is measured across a 4.0-mm side of a metal slab immersed in a magnetic field whose strength is 0.150 T. The average velocity of the charges is

A) 2.5 cm/s.
B) 5.0 cm/s.
C) 7.5 cm/s.
D) The value cannot be obtained from the information given.

Question 43

A charged particle is moving in a region where the magnetic field strength is 1.0 T directed in the +x direction and the electric field is 1500 V/m in the +y direction. The particle velocity required for a straight-line trajectory is

A) 15 km/s.
B) 2500 m/s.
C) 1500 m/s.
D) No velocity will produce a straight-line trajectory.

Question 44

A charged particle (q = 1.6 *10^-19 C) enters a mass spectrometer with a speed of 2.5 * 10⁶ m/s. The magnetic field in the spectrometer, 0.25 T, produces a circular motion of the charged particle of radius 2.5 cm. The mass of the charged particle is

A) 1.0* 10^-28 kg.
B) 2.0 *10^-28 kg.
C) 3.0 * 10^-28 kg.
D) 4.0 * 10^-28 kg.

Question 45

An electron is accelerated to an energy of 100 eV and then enters a magnetic field of strength 0.15 T. The resulting radius of the electron's trajectory is

A) 2.2 * 10^-4 m.
B) 3.3 *10^-4 m.
C) 4.4 * 10^-4 m.
D) 5.5 * 10^-4 m.

Question 46

The energy of an electron is 100eV when it enters an E * B velocity selector that utilizes a cross electric and magnetic field to produce a zero net force on the particle. The magnitude of the magnetic field is 0.085T. The magnitude of the electric field required to produce a straight-line trajectory is

A) 5.0 *10⁴ V/m.
B) 2.5 * 10⁵ V/m.
C) 5.0 * 10⁵ V/m.
D) 2.5 * 10⁶ V/m.

Question 47

An electron travels in the +x direction with a velocity of 1.5 *10⁶ m/s. It enters an E * B velocity selector that utilizes a cross electric and magnetic field to produce a zero net force on the particle. The magnitude of the magnetic field is 0.10 T in the +y direction. The magnitude of the electric field required to produce a straight-line trajectory is

A) 1.5 * 10⁵ V/m in the +z direction.
B) 1.5 *0⁵ V/m in the -z direction.
C) 1.5 * 10⁵ V/m in the +y direction.
D) 1.5 * 10⁵ V/m in the -y direction.

Question 48

The charge carriers in a metal are typically negative. A positive charge carrier

A) will not change the sign of the Hall potential.
B) will change the sign of the Hall potential.
C) will have a zero Hall potential.
D) will produce a Hall effect across the other face of the metal.

Question 49

One side of a square loop (dimensions of 15 cm *15 cm) runs parallel to a current-carrying wire I_w = 5.0 A. The distance between the side of the loop and the wire is 5.0 cm, and 3.0 A runs through the loop. The net force on the loop is

A) 1.5 $\mu$ N.
B) 6.8 $\mu$ N.
C) 13 $\mu$ N.
D) 20 $\mu$ N.

Question 50

One side of a square loop (dimensions of 15 cm * 15 cm) runs parallel to a current-carrying wire I_w = 5.0 A, and 3.0 A runs through the loop. The net force on the loop is 2.7 * 10^-6 N. The distance between the side of the loop and the wire is

A) 5.0 cm.
B) 10 cm.
C) 15 cm.
D) 20 cm.

Question 51

The magnetic dipole moment for a current I in a loop of area A is given by

A) $\mu$ = I/A.
B) $\mu$ = A/I.
C) $\mu$ = 1/(IA).
D) $\mu$ = IA.