Deck 19: Magnetic Forces and Fields

Question 1

A proton is moving at $2.0 \times 10^{7} \mathrm{~m} / \mathrm{s}$ in a magnetic field of $30 \mathrm{mT}$ . What is the magnitude of the magnetic force on the proton?

A) 0.0
B) $6.0 \times 10^{-5} \mathrm{~N}$
C) $9.6 \times 10^{-14} \mathrm{~N}$
D) $4.8 \times 10^{-14} \mathrm{~N}$
E) More information is needed.

Answer 1

More information is needed.

Question 2

A proton is moving perpendicular to a magnetic field at $3.0 \times 106 \mathrm{~m} / \mathrm{s}$ and experiences a magnetic force of magnitude $2.5 \times 10^{-16} \mathrm{~N}$ . What is the magnitude of the magnetic field?

A) $3.8 \times 10^{-2} \mathrm{~T}$
B) $1.9 \times 10^{-3} \mathrm{~T}$
C) $2.6 \times 10^{-4} \mathrm{~T}$
D) $0.52 \mathrm{~T}$
E) $5.2 \times 10^{-4} \mathrm{~T}$

Answer 2

$5.2 \times 10^{-4} \mathrm{~T}$

Question 3

An electron is moving at $2.5 \times 106 \mathrm{~m} / \mathrm{s}$ perpendicular to a uniform $3.5 \mathrm{mT}$ magnetic field. What is the radius of its path?

A) $4.1 \mathrm{~mm}$
B) $1.6 \mathrm{~cm}$
C) $3.9 \mathrm{~cm}$
D) $2.0 \mathrm{~mm}$
E) $5.1 \mathrm{~cm}$

Answer 3

$4.1 \mathrm{~mm}$

Question 4

An electron is moving at $3.0 \times 10^{6} \mathrm{~m} / \mathrm{s}$ perpendicular to a uniform magnetic field. If the radius of the motion is $18 \mathrm{~mm}$ , what is the magnitude of the magnetic field?

A) $70 \mathrm{mT}$
B) $8.9 \mathrm{nT}$
C) $1.6 \mu \mathrm{T}$
D) $9.3 \mathrm{mT}$
E) $0.95 \mathrm{mT}$

Question 5

A proton cyclotron has a magnetic field of $0.20 \mathrm{~T}$ between its poles and a radius of $0.40 \mathrm{~m}$ . What is the maximum energy for the protons from this machine?

A) $1.6 \times 10^{-13} \mathrm{~J}$
B) $4.9 \times 10^{-13} \mathrm{~J}$
C) $3.2 \times 10^{-14} \mathrm{~J}$
D) $4.9 \times 10^{-14} \mathrm{~J}$
E) $3.2 \times 10^{-13} \mathrm{~J}$

Question 6

What is the speed of a proton in a cyclotron having a $0.50 \mathrm{~T}$ magnetic field when the proton is at a distance of $25 \mathrm{~cm}$ from the center?

A) $1.1 \times 10^{4} \mathrm{~m} / \mathrm{s}$
B) $3.2 \times 10^{6} \mathrm{~m} / \mathrm{s}$
C) $3.7 \times 10^{7} \mathrm{~m} / \mathrm{s}$
D) $1.2 \times 10^{7} \mathrm{~m} / \mathrm{s}$
E) $6.0 \times 10^{6} \mathrm{~m} / \mathrm{s}$

Question 7

A proton is moving at $3.0 \times 10^{6} \mathrm{~m} / \mathrm{s}$ and experiences a magnetic force of magnitude $2.5 \times 10^{-16} \mathrm{~N}$ . If the magnetic field makes an angle of $40^{\circ}$ with respect to the velocity of the proton, what is the field's magnitude?

A) $3.3 \times 10^{-4} \mathrm{~T}$
B) $1.7 \times 10^{-4} \mathrm{~T}$
C) $4.1 \times 10^{-4} \mathrm{~T}$
D) $8.1 \times 10^{-4} \mathrm{~T}$
E) $1.6 \times 10^{-3} \mathrm{~T}$

Question 8

Find the force (magnitude and direction) exerted on an electron moving vertically upward at a speed of $2.0 \times$ $10^{7} \mathrm{~m} / \mathrm{s}$ by a horizontal magnetic field of $0.50 \mathrm{~T}$ directed north.

A) $1.6 \times 10^{-12} \mathrm{~N}$ west
B) $1.8 \times 10^{-12} \mathrm{~N}$ east
C) $1.6 \times 10^{-12} \mathrm{~N}$ east
D) $1.8 \times 10^{-12} \mathrm{~N}$ west

Question 9

An electron is moving at $3.0 \times 10^{6} \mathrm{~m} / \mathrm{s}$ at an angle of $40^{\circ}$ to a $0.80 \mathrm{~T}$ magnetic field. What is the magnitude of the force on the electron?

A) $3.8 \times 10^{-13} \mathrm{~N}$
B) $1.2 \times 10^{-13} \mathrm{~N}$
C) $2.5 \times 10^{-13} \mathrm{~N}$
D) $2.9 \times 10^{-13} \mathrm{~N}$
E) $4.8 \times 10^{-13} \mathrm{~N}$

Question 10

An electron is moving at $3.0 \times 106 \mathrm{~m} / \mathrm{s}$ at an angle of $40^{\circ}$ to a $0.80 \mathrm{~T}$ magnetic field. What is the magnitude of the acceleration of the electron?

A) $7.8 \times 1017 \mathrm{~m} / \mathrm{s}^{2}$
B) $1.4 \times 1017 \mathrm{~m} / \mathrm{s}^{2}$
C) $5.2 \times 1017 \mathrm{~m} / \mathrm{s}^{2}$
D) $9.8 \times 10^{17} \mathrm{~m} / \mathrm{s}^{2}$
E) $2.7 \times 1017 \mathrm{~m} / \mathrm{s}^{2}$

Question 11

The magnetic field in a cyclotron is $0.50 \mathrm{~T}$ . Find the magnitude of the magnetic force on a proton with velocity of $1.0 \times 10^{7} \mathrm{~m} / \mathrm{s}$ in a plane perpendicular to the field.

A) $8.0 \times 10^{-13} \mathrm{~N}$
B) $6.0 \times 10^{-13} \mathrm{~N}$
C) $6.0 \times 10^{-14} \mathrm{~N}$
D) $8.0 \times 10^{-14} \mathrm{~N}$

Question 12

The magnetic field in a cyclotron is $0.50 \mathrm{~T}$ . What is the radius of the vacuum chamber for a maximum proton velocity of $1.0 \times 10^{7} \mathrm{~m} / \mathrm{s}$ ?

A) $0.013 \mathrm{~m}$
B) $0.21 \mathrm{~m}$
C) $1.2 \mathrm{~m}$
D) $0.11 \mathrm{~m}$

Question 13

An electric field perpendicular to a magnetic field is used as a velocity selector for $\mathrm{Li}^{+}$ ions, selecting the velocity $\mathrm{v}_{1}$ . Next, $\mathrm{Li}^{++}$ ions are sent through the same velocity selector, selecting velocity $\mathrm{v}_{2}$ . If neither the electric nor magnetic fields have changed between the two processes, how do $\mathrm{v}_{1}$ and $\mathrm{v}_{2}$ compare?

A) $\mathrm{v}_{2}=\mathrm{v}_{1} / 2$
B) $v_{2}=v_{1} / 4$
C) $\mathrm{v}_{2}=\mathrm{v}_{1}$
D) $\mathrm{v}_{2}=4 \mathrm{v}_{1}$
E) $v_{2}=2 v_{1}$

Question 14

In a velocity selector for ions, when the velocity of the ions is double the value for which the selector is set, how do the magnetic force $\mathrm{F}_{\mathrm{M}}$ and the electric force $\mathrm{F}_{\mathrm{E}}$ compare?

A) $\mathrm{F}_{\mathrm{M}}=4 \mathrm{~F}_{\mathrm{E}}$
B) $\mathrm{F}_{\mathrm{M}}=1.414 \mathrm{~F}_{\mathrm{E}}$
C) $\mathrm{F}_{\mathrm{M}}=\mathrm{F}_{\mathrm{E}} / 2$
D) $F_{M}=F_{E} / 4$
E) $F_{M}=2 F_{E}$

Question 15

A flat conductor of thickness $0.500 \mathrm{~mm}$ is placed in a magnetic field of $0.200 \mathrm{~T}$ perpendicular to the flat surface. If there are $8.00 \times 1024$ charge carriers (i.e., electrons) per $\mathrm{m}^{3}$ , what is the Hall voltage generated when 3.40 A flows along the conductor?

A) $0.531 \mathrm{mV}$
B) $0.266 \mathrm{mV}$
C) $0.797 \mathrm{mV}$
D) $1.06 \mathrm{mV}$
E) $2.12 \mathrm{mV}$

Question 16

A $10 \mathrm{~m}$ long wire carrying a current of 22 A makes an angle of $37^{\circ}$ with the Earth's magnetic field of 0.51 $\mathrm{mT}$ . What is the magnetic force on the wire?

A) $0.068 \mathrm{~N}$
B) $0.011 \mathrm{~N}$
C) $0.19 \mathrm{~N}$
D) $0.090 \mathrm{~N}$
E) $0.11 \mathrm{~N}$

Question 17

If the magnetic field from a long, straight, current-carrying wire has a magnitude $\mathrm{B}_{0}$ at a distance $\mathrm{d}$ , what is the magnitude of the field at a distance $2 \mathrm{~d}$ ?

A) also $\mathrm{B}_{0}$
B) $\mathrm{B}_{0} / 2$
C) $0.693 \mathrm{~B}_{0}$
D) $\mathrm{B}_{0} / 4$
E) $0.707 \mathrm{~B}_{0}$

Question 18

A power line carries $1000 \mathrm{~A}$ at a height of $20 \mathrm{~m}$ above the ground. What is the resulting magnetic field at ground level?

A) $13 \mu \mathrm{T}$
B) $10 \mu \mathrm{T}$
C) $0.13 \mathrm{mT}$
D) $5.0 \mu \mathrm{T}$
E) $50 \mathrm{mT}$

Question 19

Two parallel wires are each carrying $10 \mathrm{~A}$ and are separated by $4.0 \mathrm{~m}$ . If the currents are in opposite directions, what is the magnitude of the magnetic field halfway between them?

A) $1.0 \mu \mathrm{T}$
B) $2.0 \mu \mathrm{T}$
C) 0.0
D) $1.4 \mu \mathrm{T}$
E) $4.0 \mu \mathrm{T}$

Question 20

If magnetic field inside a solenoid having 100 turns per $\mathrm{cm}$ and a current of $5.0 \mathrm{~A}$ is

A) $1.0 \times 10^{-4} \mathrm{~T}$ .
B) $6.3 \times 10^{-4} \mathrm{~T}$ .
C) $2.0 \times 10^{-2} \mathrm{~T}$ .
D) $1.0 \times 10^{-2} \mathrm{~T}$ .
E) $6.3 \times 10^{-2} \mathrm{~T}$

Question 21

Two long straight wires each carry a current of $12 \mathrm{~A}$ . One wire lies on the $\mathrm{x}$ -axis with its current in the positive $\mathrm{x}$ -direction. The other wire lies on the $\mathrm{y}$ -axis with its current in the positive $\mathrm{y}$ -direction. In the $\mathrm{x}-\mathrm{y}$ plane, which quadrant (quadrants) has/have points where the magnetic field is zero?

A) I
B) I and III
C) II
D) II and IV
E) none of them
F) all of them

Question 22

One wire, lying on the $x$ -axis, carries a current of $8.0 \mathrm{~A}$ in the positive $x$ -direction. Another wire, lying on the $\mathrm{y}$ -axis, carries a current of $12 \mathrm{~A}$ in the positive $\mathrm{y}$ -direction. What is the magnitude of the magnetic field at ( $\mathrm{x}$ , y) $=(8.0 \mathrm{~cm}, 12.0 \mathrm{~cm})$ ?

A) $3.0 \times 10^{-5} \mathrm{~T}$
B) $4.3 \times 10^{-5} \mathrm{~T}$
C) $1.7 \times 10^{-5} \mathrm{~T}$
D) $4.0 \times 10^{-10} \mathrm{~T}$
E) $1.3 \times 10^{-5} \mathrm{~T}$

Question 23

A solenoid of radius $1.1 \mathrm{~cm}$ , carrying a current of $2.2 \mathrm{~A}$ , produces a magnetic field at its center of $0.28 \mathrm{~T}$ . How many turns per unit length does the solenoid have?

A) $1.0 \times 10^{5} \mathrm{~m}^{-1}$
B) $1.1 \times 10^{3} \mathrm{~m}^{-1}$
C) $7.0 \times 10^{3} \mathrm{~m}^{-1}$
D) $1.0 \times 10^{-9} \mathrm{~m}^{-1}$
E) $2.2 \times 10^{3} \mathrm{~m}^{-1}$

Question 24

Find the circulation for the path shown.

A) $-(4$ A $) \mu_{0}$
B) $-\left(28\right.$ A) $\mu_{0}$
C) $(28 \mathrm{~A}) \mu_{0}$
D) $(4 \mathrm{~A}) \mu_{0}$
E) $(7 \mathrm{~A}) \mu_{0}$

Question 25

Find the circulation for the path shown.

A) $\left(4\right.$ A) $\mu_{0}$
B) $-(28 \mathrm{~A}) \mu_{0}$
C) $(28 \mathrm{~A}) \mu_{0}$
D) $-(4 \mathrm{~A}) \mu_{0}$
E) $-(7 \mathrm{~A}) \mu_{0}$

Question 26

A proton and electron, each travelling with the same velocity, enter a region of uniform magnetic field. They experience

A) forces in the same direction and having ratio $\mathrm{F}_{\mathrm{p}} / \mathrm{F}_{\mathrm{e}}=\mathrm{m}_{\mathrm{e}} / \mathrm{m}_{\mathrm{p}}$ .
B) the same force.
C) forces equal in magnitude, but opposite in direction.
D) forces opposite in direction and having ratio $\mathrm{F}_{\mathrm{p}} / \mathrm{F}_{\mathrm{e}}=\mathrm{m}_{\mathrm{e}} / \mathrm{m}_{\mathrm{p}}$ .

Question 27

A proton and electron, travelling with the same velocity in the $+x$ direction, enter separate regions, each with a uniform magnetic field in the $\pm \mathrm{y}$ direction (magnitude $\mathrm{B}_{\mathrm{p}}$ for the proton, $\mathrm{B}_{\mathrm{e}}$ for the electron). They each experience the same acceleration. What can we conclude?

A) The magnetic fields were in the same direction and have ratio $B_{p} / B_{e}=m_{e} / m_{p}$ .
B) The magnetic fields were in the opposite direction and have ratio $B_{p} / B_{e}=m_{p} / m_{e}$ .
C) The magnetic fields were identical in magnitude and direction.
D) The magnetic fields were in the opposite direction and have ratio $B_{p} / B_{e}=m_{e} / m_{p}$ .
E) The magnetic fields were identical in magnitude and opposite in direction.
F) The magnetic fields were in the same direction and have ratio $B_{p} / B_{e}=m_{p} / m_{e}$ .

Question 28

A proton and electron, each travelling with the same velocity in the $+x$ direction, enter a region of uniform magnetic field in the $+y$ direction. If the acceleration of the electron is $a$ in the $+z$ direction, what is the acceleration of the proton?

A) $a \mathrm{~m}_{\mathrm{p}} / \mathrm{m}_{\mathrm{e}}$ in the $-\mathrm{z}$ direction
B) $a \mathrm{~m}_{\mathrm{p}} / \mathrm{m}_{\mathrm{e}}$ in the $+\mathrm{z}$ direction
C) $a$ in the $-\mathrm{z}$ direction
D) $a$ in the $+\mathrm{z}$ direction
E) $a \mathrm{~m}_{\mathrm{e}} / \mathrm{m}_{\mathrm{p}}$ in the $+\mathrm{z}$ direction
F) $a \mathrm{~m}_{\mathrm{e}} / \mathrm{m}_{\mathrm{p}}$ in the $-\mathrm{z}$ direction

Question 29

A cyclotron is designed to accelerate protons (mass $1.67 \times 10^{-27} \mathrm{~kg}$ ) up to a kinetic energy of $2.5 \times 10^{-13} \mathrm{~J}$ . If the magnetic field in the cyclotron is $0.75 \mathrm{~T}$ , what is the radius of the dipole magnets in the cyclotron?

A) $5.8 \mathrm{~cm}$
B) $14 \mathrm{~cm}$
C) $24 \mathrm{~cm}$
D) $17 \mathrm{~cm}$

Question 30

A cyclotron is designed to accelerate protons (mass $1.67 \times 10^{-27} \mathrm{~kg}$ ) up to a kinetic energy of $2.5 \times 10^{-13} \mathrm{~J}$ . If the radius of the dipole magnets is $96 \mathrm{~cm}$ , what is the magnetic field used in the cyclotron?

A) $0.13 \mathrm{~T}$
B) $0.21 \mathrm{~T}$
C) $35 \mathrm{mT}$
D) $0.19 \mathrm{~T}$

Question 31

A cyclotron is designed to accelerate protons to a maximum kinetic energy K. Assuming one then tried to accelerate alpha particles (about four times the mass and twice the charge), what kinetic energy could be achieved?

A) $2 \mathrm{~K}$
B) $1 / 2 \mathrm{~K}$
C) $4 \mathrm{~K}$
D) $\mathrm{K}$
E) $1 / 4 \mathrm{~K}$
F) $8 \mathrm{~K}$

Question 32

A charged particle of mass $1.0 \times 10^{-26} \mathrm{~kg}$ enters a region of uniform magnetic field at a speed of $2.8 \times 10^{6}$ $\mathrm{m} / \mathrm{s}$ , at an angle of 37 degrees relative to the magnetic field direction. If the magnetic field strength is $1.2 \mathrm{~T}$ and the charge of the particle is $+\mathrm{e}$ , what will be the radius of the helical path it takes?

A) $11 \mathrm{~cm}$
B) Insufficient information is given.
C) $8.8 \mathrm{~cm}$
D) $15 \mathrm{~cm}$

Question 33

A charged particle of mass $1.0 \times 10^{-26} \mathrm{~kg}$ enters a region of uniform magnetic field at a speed of $2.8 \times 10^{6}$ $\mathrm{m} / \mathrm{s}$ , at an angle of 37 degrees relative to the magnetic field direction. If the magnetic field strength is $1.2 \mathrm{~T}$ what will be the radius of the helical path it takes?

A) $8.9 \mathrm{~cm}$ .
B) $15 \mathrm{~cm}$
C) $11 \mathrm{~cm}$
D) Insufficient information given.