Deck 26: Magnetic Field and Magnetic Forces

Question 1

The figure shows a velocity selector that can be used to measure the speed of a charged particle. A beam of particles is directed along the axis of the instrument. A parallel plate capacitor sets up an electric field E, which is oriented perpendicular to a uniform magnetic field B. If the plates are separated by 2.0 mm and the value of the magnetic field is 0.60 T, what voltage between the plates will allow particles of speed 5.0 × 10⁵ m/s to pass straight through without deflection?

A) 600 V
B) 1900 V
C) 3800 V
D) 190 V
E) 94 V

Answer 1

600 V

Question 2

An alpha particle is moving at a speed of 5.0 × 10⁵ m/s in a direction perpendicular to a uniform magnetic field of strength 0.040 T. The charge on an alpha particle is 3.2 × 10^-19 C and its mass is 6.6 × 10^-27 kg.
(a) What is the radius of the path of the alpha particle?
(b) How long does it take the alpha particle to make one complete revolution around its path?

Answer 2

(a) 0.26 m
(b) 3.2 µs

Question 3

Three particles travel through a region of space where the magnetic field is out of the page, as shown in the figure. The electric charge of each of the three particles is, respectively,

A) 1 is neutral, 2 is negative, and 3 is positive.
B) 1 is neutral, 2 is positive, and 3 is negative.
C) 1 is positive, 2 is neutral, and 3 is negative.
D) 1 is positive, 2 is negative, and 3 is neutral.
E) 1 is negative, 2 is neutral, and 3 is positive.

Answer 3

1 is negative, 2 is neutral, and 3 is positive.

Question 4

As shown in the figure, a small particle of charge q = -7.0 × 10^-6 C and mass m = 3.1 × 10^-12 kg has velocity v₀ = 9.4 × 10³ m/s as it enters a region of uniform magnetic field. The particle is observed to travel in the semicircular path shown, with radius R = 5.0 cm. Calculate the magnitude and direction of the magnetic field in the region.

Question 5

A proton, with mass 1.67 × 10^-27 kg and charge +1.6 × 10^-19 C, is sent with velocity 7.1 × 10⁴ m/s in the +x direction into a region where there is a uniform electric field of magnitude 730 V/m in the +y direction. What are the magnitude and direction of the uniform magnetic field in the region, if the proton is to pass through undeflected? Assume that the magnetic field has no x-component and neglect gravitational effects.

Question 6

Ions having equal charges but masses of M and 2M are accelerated through the same potential difference and then enter a uniform magnetic field perpendicular to their path. If the heavier ions follow a circular arc of radius R, what is the radius of the arc followed by the lighter?

A) 4R
B) 3R
C) R
D) R/
E) R/2

Question 7

A proton is first accelerated from rest through a potential difference V and then enters a uniform 0.750-T magnetic field oriented perpendicular to its path. In this field, the proton follows a circular arc having a radius of curvature of 1.84 cm. What was the potential difference V? (mproton = 1.67 × 10^-27 kg, e = 1.60 × 10^-19 C)

Question 8

A charged particle is moving with speed v perpendicular to a uniform magnetic field. A second identical charged particle is moving with speed 2v perpendicular to the same magnetic field. If the frequency of revolution of the first particle is f, the frequency of revolution of the second particle is

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

Question 9

An electron moving with a velocity = 5.0 × 107 m/s î enters a region of space where perpendicular electric and a magnetic fields are present. The electric field is
= ĵ) What magnetic field will allow the electron to go through the region without being deflected?

A) = +2.0 × 10^-4 T ĵ
B) = -2.0 × 10^-4 T ĵ
C) = +2.0 × 10^-4 T

D) = -2.0 × 10^-4 T

E) = +5.0 × 10^-4 T

Question 10

An electron moving in the direction of the +x-axis enters a magnetic field. If the electron experiences a magnetic deflection in the -y direction, the direction of the magnetic field in this region points in the direction of the

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

Question 11

A particle with charge -5.00 C initially moves at = (1.00 î + 7.00 ĵ ) m/s. If it encounters a magnetic field
Find the magnetic force vector on the particle.

A) (-350 î + 50.0 ĵ ) N
B) (-350 î - 50.0 ĵ ) N
C) (350 î + 50.0 ĵ ) N
D) (350 î - 50.0 ĵ ) N

Question 12

A beam of electrons is accelerated through a potential difference of 10 kV before entering a region having uniform electric and magnetic fields that are perpendicular to each other and perpendicular to the direction in which the electron is moving. If the magnetic field in this region has a value of 0.010 T, what magnitude of the electric field is required if the particles are to be undeflected as they pass through the region?

A) 2.3 × 10³ V/m
B) 7.9 × 10³ V/m
C) 5.9 × 10⁵ V/m
D) 6.0 × 10⁵ V/m
E) 7.2 × 10⁶ V/m

Question 13

A charge is accelerated from rest through a potential difference V and then enters a uniform magnetic field oriented perpendicular to its path. The field deflects the particle into a circular arc of radius R. If the accelerating potential is tripled to 3V, what will be the radius of the circular arc?

A) 9R
B) 3R
C) R
D) R/
E) R/9

Question 14

A wire in the shape of an "M" lies in the plane of the paper. It carries a current of 2.0 A, flowing from points A to E, as shown in the figure. It is placed in a uniform magnetic field of 0.75 T in the same plane, directed as shown on the right side of the figure. The figure indicates the dimensions of the wire. What are the magnitude and direction of the force acting on
(a) section AB of this wire?
(b) section BC of this wire?
(c) section CD of this wire?
(d) section DE of this wire?
(e) the entire wire?

Question 15

An electron moves with a speed of 8.0 × 10⁶ m/s along the +x-axis. It enters a region where there is a magnetic field of 2.5 T, directed at an angle of 60° to the +x-axis and lying in the xy-plane. (1 eV = 1.60 × 10^-19 C, ^mel = 9.11 × 10^-31 kg) Calculate the magnitude of
(a) the magnetic force on the electron.
(b) the acceleration of the electron.

Question 16

A vertical wire carries a current vertically upward in a region where the magnetic field vector points toward the north. What is the direction of the magnetic force on this current due to the field?

A) downward
B) toward the north
C) toward the south
D) toward the east
E) toward the west

Question 17

A uniform magnetic field of magnitude 0.80 T in the negative z-direction is present in a region of space, as shown in the figure. A uniform electric field is also present. An electron that is projected with an initial velocity v₀ = 9.1 × 10⁴ m/s in the positive x-direction passes through the region without deflection. What is the electric field vector in the region?

A) -73 kV/m ĵ
B) +73 kV/m î
C) +110 kV/m î
D) +110 kV/m ĵ
E) -110 kV/m ĵ

Question 18

An electron enters a magnetic field of 0.75 T with a velocity perpendicular to the direction of the field. At what frequency does the electron traverse a circular path? (mel = 9.11 × 10^-31 kg, e = 1.60 × 10^-19 C)

A) 2.1 × 10¹⁰ Hz
B) 4.8 × 10^-7 Hz
C) 2.1 × 10¹⁴ Hz
D) 4.8 × 10^-11 Hz

Question 19

A charged particle of mass 0.0020 kg is subjected to a 6.0 T magnetic field which acts at a right angle to its motion. If the particle moves in a circle of radius 0.20 m at a speed of 5.0 m/s, what is the magnitude of the charge on the particle?

A) 0.0083 C
B) 120 C
C) 0.00040 C
D) 2500 C

Question 20

An electron, moving toward the west, enters a uniform magnetic field. Because of this field the electron curves upward. The direction of the magnetic field is

A) towards the north.
B) towards the south.
C) towards the west.
D) upward.
E) downward.

Question 21

A thin copper rod that is 1.0 m long and has a mass of 0.050 kg is in a magnetic field of 0.10 T. What minimum current in the rod is needed in order for the magnetic force to cancel the weight of the rod?

A) 1.2 A
B) 2.5 A
C) 4.9 A
D) 7.6 A
E) 9.8 A

Question 22

A wire along the z-axis carries a current of 6.8 A in the +z direction. Find the magnitude and direction of the force exerted on a 6.1-cm long length of the wire by a uniform magnetic field with magnitude 0.36 T in the -x direction.

Question 23

A circular coil of wire of 200 turns and diameter 2.0 cm carries a current of 4.0 A. It is placed in a magnetic field of with the plane of the coil making an angle of 30° with the magnetic field. What is the magnetic torque on the coil?

A) 0.15 N ∙ m
B) 0.088 N ∙ m
C) 0.29 N ∙ m
D) 0.40 N ∙ m
E) 0.076 N ∙ m

Question 24

A straight wire that is 0.60 m long is carrying a current of 2.0 A. It is placed in a uniform magnetic field of strength 0.30 T. If the wire experiences a force of 0.18 N, what angle does the wire make with respect to the magnetic field?

A) 25°
B) 30°
C) 35°
D) 60°
E) 90°

Question 25

A rigid rectangular loop, which measures 0.30 m by 0.40 m, carries a current of 5.5 A, as shown in the figure. A uniform external magnetic field of magnitude 2.9 T in the negative x direction is present. Segment CD is in the xz-plane and forms a 35° angle with the z-axis, as shown. Find the magnitude of the external torque needed to keep the loop in static equilibrium.

A) 1.1 N ∙ m
B) 0.73 N ∙ m
C) 1.3 N ∙ m
D) 1.4 N ∙ m
E) 1.6 N ∙ m

Question 26

A circular loop of diameter 10 cm, carrying a current of 0.20 A, is placed inside a magnetic field = 0.30 T
) The normal to the loop is parallel to a unit vector
= -0.60 î - 0.80 ĵ. Calculate the magnitude of the torque on the loop due to the magnetic field.

A) 4.7 × 10^-4 N ∙ m
B) 2.8 × 10^-4 N ∙ m
C) 0.60 × 10^-4 N ∙ m
D) 1.2 × 10^-4 N ∙ m
E) zero

Question 27

A rigid circular loop has a radius of 0.20 m and is in the xy-plane. A clockwise current I is carried by the loop, as shown. The magnitude of the magnetic moment of the loop is 0.75 A ∙ m². A uniform external magnetic field, B = 0.20 T in the positive x-direction, is present.
(a) What is the current in the loop?
(b) Find the magnitude of the magnetic torque exerted on the loop.
(c) If the loop is released from rest, in what direction will points a and c initially move?

Question 28

An L-shaped metal machine part is made of two equal-length segments that are perpendicular to each other and carry a 4.50-A current as shown in the figure. This part has a total mass of 3.80 kg and a total length of 3.00 m, and it is in an external 1.20-T magnetic field that is oriented perpendicular to the plane of the part, as shown. What is the magnitude of the NET magnetic force that the field exerts on the part?

A) 8.10 N
B) 11.5 N
C) 16.2 N
D) 22.9 N
E) 32.4 N

Question 29

A rectangular loop of wire carrying a 4.0-A current is placed in a magnetic field of 0.60 T. The magnitude of the torque acting on this wire when the plane of the loop makes a 30° angle with the field is measured to be 1.1 N ∙ m. What is the area of this loop?

A) 0.20 m²
B) 0.40 m²
C) 0.26 m²
D) 0.80 m²
E) 0.53 m²

Question 30

A rigid circular loop has a radius of 0.20 m and is in the xy-plane. A clockwise current I is carried by the loop, as shown. The magnitude of the magnetic moment of the loop is 0.75 A ∙ m². A uniform external magnetic field, B = 0.20 T in the positive x-direction, is present. An external torque changes the orientation of the loop from one of lowest potential energy to one of highest potential energy. The work done by this external torque is closest to

A) 0.20 J
B) 0.30 J
C) 0.40 J
D) 0.50 J
E) 0.60 J

Question 31

A wire carries a 4.0-A current along the +x-axis through a magnetic field = (5.0 î + 7.0 ĵ) T. If the wire experiences a force of 30 N
As a result, how long is the wire?

A) 1.1 m
B) 0.87 m
C) 1.5 m
D) 0.63 m

Question 32

A straight 15.0-g wire that is 2.00 m long carries a current of 8.00 A. This wire is aligned horizontally along the west-east direction with the current going from west to east. You want to support the wire against gravity using the weakest possible uniform external magnetic field.
(a) Which way should the magnetic field point?
(b) What is the magnitude of the weakest possible magnetic field you could use?

Question 33

A wire segment 1.2 m long carries a current I = 3.5 A, and is oriented as shown in the figure. The +x-axis points directly into the page. A uniform magnetic field of magnitude 0.50 T pointing toward the -x direction is present as shown. What is the magnetic force vector on the wire segment?

A) (+1.1 ĵ - 1.8 ) N
B) (-1.1 ĵ + 1.8 ) N
C) (-1.1 ĵ - 1.8 ) N
D) (+1.8 ĵ - 1.1 ) N
E) (-1.8 ĵ + 1.1 ) N

Question 34

A round loop of diameter 12 cm, carrying a current of 0.40 A, is placed inside a magnetic field = 0.20 T î + 0.40 T ĵ. The normal to the loop is parallel to the unit vector
= -0.60 î - 0.80 ĵ. What is the potential energy of the loop?

A) -4.5 × 10^-3 J
B) +2.0 × 10^-3 J
C) -2.0 × 10^-3J
D) -2.3 × 10^-3J
E) +4.5 × 10^-3 J

Question 35

A 15-turn rectangular loop of wire of width 10 cm and length 20 cm has a current of 2.5 A flowing through it. Two sides of the loop are oriented parallel to a uniform magnetic field of strength 0.037 T, and the other two sides are perpendicular to the magnetic field.
(a) What is the magnitude of the magnetic moment of the loop?
(b) What torque does the magnetic field exert on the loop?

Question 36

A wire segment 1.2 m long carries a current I = 3.5 A and is oriented as shown in the figure. A uniform magnetic field of magnitude 0.50 T pointing toward the -x direction is present as shown. The +z-axis points directly into the page. What is the magnetic force vector on the wire segment?

A) +1.6 N ĵ
B) -1.6 N
C) +1.6 N
D) (+1.3 ĵ - 1.6 ) N
E) (-1.3 ĵ + 1.6 N