Chapter28.Magnetic

Dr. M. F. Al-Kuhaili – PHYS 102 – Chapter 28 Page 1

PHYS102 Previous Exam Problems –

CHAPTER

28

Magnetic Fields

Magnetic force on a particle Crossed fields Circulating charge Magnetic force on a wire Loops, dipole moment & torque

1. A particle (mass = 6.0 mg) moves with a speed of 4.0 km/s in the xy plane in a direction that makes an

angle of 37° above the positive x axis. At the instant it enters a magnetic field of 5.0×10-3 i (T), it experiences

an acceleration of 8.0 k (m/s2

2. A square loop of side 0.20 m consists of 50 closely wrapped turns, each carrying a current of 0.50 A. As

shown in figure 1, the loop is oriented in a uniform magnetic field of 0.40 T directed in the positive y direction.

What is the magnitude of the torque on the loop? (Ans: 0.35 N.m)

). What is the charge of the particle? (Ans: – 4.0 µC)

3. Figure 2 shows a loop of wire carrying a current of 2.0 A. The loop has the shape of a right-angle triangle

with two equal sides, each 20 cm long. A 1.5-T uniform magnetic field is parallel to the hypotenuse. What is the

magnitude of the resultant magnetic force on the two equal sides? (Ans: zero)

4. An ion with a charge of +4.8×10−19 C is in a region where a uniform electric field of 6.0×104

(Ans: 3.3×10

V/m is

perpendicular to a uniform magnetic field of 1.8 T. If its acceleration is zero, what is its speed? 4

5. A 2.0-C charge moves in a uniform magnetic field with a velocity of (2.0

m/s)

i + 4.0 j ) m/s and experiences a

magnetic force of 12 N along the + z-axis. The x component of the magnetic field is equal to zero. Determine the

y component of the magnetic field. (Ans: +3.0 T)

6. A charged particle has a kinetic energy of 10-7 joules and moves in a circular path in a uniform magnetic

field. If the magnitude of the magnetic force on the particle is 1.5×10-4

7. What is the kinetic energy of an electron that passes in a straight line through perpendicular electric and

magnetic fields if E = 4.0 kV/m and B = 8.0 mT? [1 eV = 1.6×10-19 J] (Ans: 0.71 eV)

N, what is the radius of the circular

motion? (Ans: 1.3 mm)

8. A potential difference of 600 V is applied to accelerate an electron from rest. This accelerated electron

enters a uniform magnetic field and completes one revolution in 9 ns. Determine the radius of the electron orbit?

(Ans: 0.021 m)

9. An electron with velocity v = (4.0×104 i + 3.0×106 j ) m/s enters a region of magnetic field B = 0.40 i T.

What is the magnetic force on the electron? (Ans: 1.9×10-13 k N)


10. A 300-turn square loop, having a side length of 6 cm, carries a current of 15 A. The loop is placed in an

external magnetic field of magnitude 3.0 T. Determine the magnitude of the maximum torque exerted on the

loop. (Ans: 49 N.m)

11. An electron moving perpendicular to a 50-µT magnetic field goes through a circular trajectory. What is

the time required to complete one revolution? (Ans: 7.15×10-7

12. A 100-turns coil, with an area of 2.0 m

s) 2

13. Figure 5 shows a proton moving at a constant speed of 300 m/s along the negative x axis through uniform

electric and magnetic fields. The electric field is directed along the positive y direction and has a magnitude of

900 N/C. What is the magnitude and direction of the magnetic field? (Ans: 3.0 T, along the negative z axis)

, lies in the xz plane and carries a current I = 0.3 A in the direction

indicated in figure 4. The coil lies in a magnetic field directed along the x axis and has a magnitude of 1.5 T.

What is magnitude and direction of the torque on the coil? (Ans: 90 N.m along the positive z axis)

14. What is the angle between a 1.0-mT uniform magnetic field and the velocity of an electron, if the electron

has an acceleration of 7.0×1012 m/s2

and a speed of 7.0×104

m/s?(Ans: 35o

15. A wire lying along the y axis from y = 0 to y = 0.36 m carries a current of 2.0 mA in the negative y

direction. The wire fully lies in a uniform magnetic field given by B = 0.36

)

i + 0.46 j T. What is the magnetic

force on the wire? (Ans: 2.6×10-4

16. A uniform magnetic field of 2.0 T along the positive z axis crosses an electric field E. What is the electric

field needed to guide an electron with a speed of 40 km/s along a straight line in the positive x axis direction?

(Ans: 80 kV/m along the positive y axis)

N in the positive z direction)

17. In figure 6, an electron of speed 2.0×105

(Ans: 6.4×10

m/s moves along positive x axis in a uniform magnetic field of

magnitude 0.2 T pointing into the page (–z direction). What is the magnetic force on the electron? -15

18. In a uniform magnetic field, a particle of charge 1.5 µC and mass 2.0 µg completes 5 revolutions in one

second. What is the magnitude of the magnetic field? (Ans: 42 mT)

N, -y axis)

19. A straight wire of linear mass density 100 g/m is located perpendicular to a magnetic field of 0.5 T, as

shown in the figure 7. What current in the wire is needed to balance the gravitational force on the wire?

(Ans: 2.0 A to the right)

20. In figure 8, an electron moves toward the west at a speed of 1.0×107 m/s in a downward (normal into the

page) uniform magnetic field of magnitude 3.0×10-4

(Ans: 4.8×10

T. What is the magnetic force on the electron? -16

21. The plane of a rectangular loop wire is parallel to a 2.0-T magnetic field. The loop has an area of 4.0 cm

N, north) 2

and carries a current of 6.0 A. Calculate the magnitude of the torque that acts on the loop. (Ans: 4.8×10-3

22. In figure 10, a rectangular loop, L

N.m)

1 = 2.0 cm by L2 = 3.0 cm, carrying a current I = 0.1 A, is suspended

from a spring of spring constant k = 8.0×10-2

23. An electron, that has velocity v = 3.2×10

N/m. The loop is placed into a uniform magnetic field, which

points into the page, and the spring is observed to stretch 1.0 cm. What is the magnitude of the magnetic field?

[Neglect the mass of the loop] (Ans: 0.4 T) 7 i (m/s), travels parallel to a uniform magnetic field of strength

2.60×10-3

24. What uniform magnetic field, applied perpendicular to a beam of electrons moving at 1.4×10

T. What is the force on the electron? (Ans: zero) 6 m/s is

required to make the electrons travel in a circular orbit of radius 0.40 m? (Ans: 2.0×10-5 T)


25. In figure 12, a loop of wire carrying a current, I = 2.0 A is in the shape of a right triangle with two equal

sides, each 15 cm long. A 0.7-T uniform magnetic field is in the plane of the triangle and is perpendicular to the

hypotenuse. What is the resultant magnetic force on the two equal sides? (Ans: 0.30 N, into the page)

26. A wire of total length 4L and carrying a current I is placed in a uniform magnetic field B that is directed

out of the page, as shown in figure 14. Determine the net magnetic force on the wire. (Ans: 2ILB down)

27. A wire bent into a semicircle of radius R = 2.0 m forms a closed circuit and carries a current of 1.5 A. The

circuit lies in the xy plane, and a uniform magnetic field B = 3.0 T is present along the y axis, as shown in

figure 15. Find the magnitude of the magnetic force on the curved portion of the wire. (Ans: 18 N)

28. A straight long wire having a total length 2L = 10 cm is carrying a current of 10 A. The wire is bent at its

mid point to form an angle of 90°, with each side of length L. As shown in figure 17, the wire is placed in the xy

plane in a region where a constant magnetic field of magnitude 3.0 mT, out of the page, exists. What is the

magnitude of the magnetic force on this wire? (Ans: 2.1 mN)

29. A long straight wire carries a 6.0-A current that is directed in the positive x direction. When a uniform

magnetic field is applied perpendicular to a 3.0-m segment of the wire, the magnetic force on the segment is

0.36 N, directed in the negative y direction, as shown in figure 19. What is the magnetic field?

(Ans: 20 mT out of the page)

30. Figure 20 shows a 20-turn rectangular coil of dimensions 10 cm by 5.0 cm. It carries a current of 0.10 A,

and is hinged along one long side. There is a uniform magnetic field in the region given by: B = 0.50 i T. In unit

vector notation what is the torque acting on the coil about the hinge line? (Ans: -5.0×010-3 k N.m)

31. A proton is moving with velocity of v = (1.5 i + 1.5 j )×106 m/s. It enters a region of a uniform magnetic

field pointing in the negative z direction. What is the direction of a uniform electric field in the xy plane that

will make the proton move un-deflected? (Ans: At an angle of 315o

32. A particle, with charge q = + 1.6×10

form the positive x axis) −16 C and mass m = 3.2×10−27 kg, is travelling in the positive y

direction at speed v = 5.0×106

(Ans: 0.20 mT, into the page)

m/s, as shown in figure 21. It enters a region of uniform magnetic field where it is

deflected to follow a circular path of radius R = 0.50 m. What is the magnetic field in this region?

33. In figure 22, a square loop of wire of side 0.50 m lies in the xy plane. The current in the loop is 0.25 A.

There is a uniform magnetic field B in the positive y direction of magnitude 0.75 T. What is the toque on the

loop? (Ans: 0.047 N.m, causing rotation about the line PQ)

34. A circular loop of radius 10 cm carries a current of 20 A. The magnetic moment of the loop is directed

along the unit vector 0.60 i + 0.80 j . The magnetic field is B = 0.20 i – 0.40 j (T). Find the torque on the loop.

(Ans: – 0.25 k N.m)

35. The parallel plates shown in figure 25 are 3.8 cm apart. A 0.064-T magnetic field is present in the space

between the plates perpendicular to the plane of the paper. When an electron travelling horizontally with a speed

of 5.1×105

36. A proton moves through uniform magnetic and electric fields. The magnetic field is B = -3.0

m/s enters the region, it passes through un-deflected. What is the potential difference between the

plates? (Ans: 1.24 kV)

i (mT) and

the electric field is E = +4.0 k (V/m). At one instant, the velocity of the proton is v = +250 j (m/s). At that

instant, what is the magnitude of the net force on the proton? (Ans: 7.6×10-19 N)


37. A wire 72 cm in length has a mass of 15 g. It is suspended by a pair of flexible leads in a magnetic field B

= 0.54 T, pointing out of the page, as shown in figure 27. What current must exist in the wire for the tension in

the supporting leads to be zero? (Ans: 0.38 A from Q to P)

38. A loop of wire carrying a current of 2.0 A is in the shape of a right-angle triangle with two equal sides,

each 15 cm long. A 0.70-T uniform magnetic field is in the plane of the triangle and is directed as shown in

figure 28. What is the magnetic force on side 3? (Ans: 0.21 N, into of the page)

39. A closed loop has an area of 5.8×10-2 m2, and carries a current of 3.0 A. It is placed in an external

magnetic field, whose magnitude is 0.50 T, with its dipole moment initially making an angle of 90o

40. A 2.0-C charge moves with a velocity of v = 4.0

with the

external magnetic field. How much work is done by the magnetic field as it rotates the loop from its initial

orientation to a final orientation where the dipole moment is aligned with the field? (Ans: +0.087 J)

i + 6.0 j (m/s), and experiences a magnetic force of

FB i = 24 – 16 j + 24 k (N) in a magnetic field B = By j + 2.0 k (T). Calculate By

41. A wire of length 2.0 m carries a current of 2.0 A in the direction of the positive y axis. The wire is placed

in a uniform magnetic field. To produce a maximum magnetic force of 1.0 N directed along the positive x axis,

what must be the magnetic field? (Ans: 0.25 T along the positive z direction)

? (Ans: 3.0 T)

42. An electron with a kinetic energy of 8.0×10-17 J and a second electron with a kinetic energy of 4.8×10-17

43. A conducting wire formed into the shape of an M, with dimensions as shown in figure 29, carries a current

of 15 A. An external magnetic field B = 2.5 T is directed, as shown, throughout the region occupied by the

conductor. Calculate the magnitude of the net magnetic force exerted on the conductor by the magnetic field, if

L = 2.00 cm. (Ans: 1.1 N)

J

are moving in a uniform magnetic field in circular orbits in a plane perpendicular to a magnetic field. What is

the ratio of the radius of the orbit of the first electron to that of the second electron? (Ans: 1.3)

44. Figure 30a shows two concentric coils, lying in the same plane, carry currents in opposite directions. The

current in the larger coil 1 is fixed. Current i2 in coil 2 can be varied. Figure 30b gives the net magnetic moment

of the two-coil system as a function of i2. If the current in coil 2 is then reversed, what is the magnitude of the

net magnetic moment of the two-coil system when i2 = 8.0 mA? (Ans: 5.2×10-5 A.m2

45. A proton moves around a circular path (radius = 2.0 mm) in a uniform 0.25 T magnetic field. What total

distance does this proton travel during a 1.0-s time interval? (Ans: 48 km)

)


A B C D E Conceptual Problems 1. A current loop is oriented in three different positions relative to a uniform magnetic field. In position 1, the

plane of the loop is perpendicular to the field lines. In positions 2 and 3, the plane of the loop is parallel to the

field lines as shown in figure 3. The torque is maximum in: A. positions 2 and 3

B. position 1

C. position 2

D. position 3

E. all three positions

2. 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. The frequency of revolution

of the first particle is f. The frequency of revolution of the second particle is: A. f

B. 4f

C. f/2

D. 2f

E. f/4

3. An electron enters a region that contains a magnetic field directed into the page as shown in figure 9. The

velocity of the electron makes an angle of 30o

A. at an angle of 30

with the +y axis. What is the direction of the magnetic force on

the electron when it enters the field? O

B. upwards and out of the page.

below the positive x axis and in the plane of the page.

C. at an angle of 30O

D. at an angle of 60

above the positive x axis and in the plane of the page. O

E. at an angle of 60

above the positive x axis and in the plane of the page. O

4. A charged particle is projected with velocity v into a region where there exists a uniform electric field of

strength E perpendicular to a uniform magnetic field of strength B. If the velocity of the charged particle is to

remain constant, the minimum velocity must be:

below the positive x axis and in the plane of the page.

A. of magnitude E/B and perpendicular to both E and B.

B. of magnitude E/B and parallel to B.

C. of magnitude E/B and parallel to E.

D. of any magnitude but at 45 degrees to both E and B.

E. of magnitude B/E and perpendicular to both E and B.

5. For a charged particle moving in a magnetic field, the magnetic field can (1) change its velocity.

(2) change its speed.

(3) change its acceleration.

(4) change its kinetic energy.

A. 1 and 3 only.

B. 1 and 2 only.

C. 1, 2, 3, and 4.

D. 3 and 4 only.

E. 4 only.


6. A charged particle is placed in a region of space and it experiences a force only when it is in motion. It can

be concluded that the region encloses: A. A magnetic field only.

B. An electric field only.

C. Both a magnetic field and an electric field.

D. Both a magnetic field and a gravitational field.

E. Both a gravitational field and an electric field.

7. Which one of the following statements is false? A uniform magnetic field A. changes the kinetic energy of a charge.

B. exerts a force on a moving charge.

C. accelerates a moving charge.

D. of the earth is a measurable quantity.

E. changes the momentum of a moving charge. 8. Figure 11 shows the circular paths of an electron and a proton that travel at the same speed in a uniform

magnetic field B, which points into the page. (a) Which particle follows the bigger circle, and (b) does that

particle travel clockwise or counterclockwise? A. (a) proton (b) counterclockwise

B. (a) proton (b) clockwise

C. (a) electron (b) counterclockwise

D. (a) electron (b) clockwise

E. Not enough information given.

9. The path of a charged particle in a magnetic field when its direction of motion is not at right angle to the

magnetic field, will be a: A. helix.

B. circle.

C. parabola.

D. straight line.

E. hyperbola. 10. What is the initial direction of the deflection of an electron, initially moving in the y direction as it enters

the magnetic field shown in figure 13? [The magnetic field is in the xy plane and makes an angle of 45o

A. out of the page.

with the

x axis].

B. y direction.

C. 45o

D. 45

with the x direction. o

E. into the page.

with the y direction.

11. Which of the following is the correct statement? A. The magnetic force on a charged particle could never be in the

direction of its velocity.

B. The magnetic force does work on a moving charge.

C. The kinetic energy of a charged particle increases in a constant magnetic field.

D. The acceleration of a charged particle under constant magnetic field is zero.

E. The magnetic force does exist on a static charge.


12. A horizontal, long current-carrying wire is hanging from a vertical thread. The current is oriented into the

plane of figure 16. A uniform magnetic field is applied and the wire is pulled away from the vertical. Which of

the arrows labeled A to D correctly indicates the direction of the magnetic field? A. C

B. A

C. D

D. B

E. The magnetic field is oriented into the plane of the picture.

13. Figure 18 shows five situations in which a positively charged particle moves at velocity v through a

uniform magnetic field B and experiences a magnetic force FB

A. II

. Which of the five situations is possible?

B. III

C. I

D. V

E. IV

14. In figure 23, a copper wire AB is hanging between the poles of a magnet. As a result of closing the switch

(S), there will be A. A magnetic force on the wire AB into the page.

B. A magnetic force on the wire AB out of the page.

C. A magnetic force on the wire AB towards the left.

D. A magnetic force on the wire AB towards the right.

E. No magnetic force on the wire AB.

15. An electron enters a region of uniform perpendicular E and B fields. It is observed that the velocity v of

the electron is unaffected. A possible explanation is A. v is perpendicular to both E and B has a magnitude of E/B.

B. v is parallel to E and has a magnitude of E/B.C. v is parallel to B.

D. v is perpendicular to both E and B has a magnitude of B/E.

E. v is parallel to E and has a magnitude of B/E. 16. A uniform magnetic field is directed into the page. A particle, moving in the plane of the page, follows a

clockwise spiral of decreasing radius as shown in figure 24. A reasonable explanation is that the particle has A. a negative charge and is slowing down.

B. a positive charge and is slowing down.

C. a positive charge and is speeding up.

D. a negative charge and is speeding up.

E. a positive charge and is moving at constant speed.

17. The magnetic force on a point charge in a magnetic field is largest for a given speed when it: A. moves perpendicular to the magnetic field.

B. moves in the direction of the magnetic field.

C. moves in a direction opposite to the magnetic field.

D. has velocity components both parallel and perpendicular to the field.

E. has velocity components both perpendicular and anti-parallel to the field.


18. Two particles move through a uniform magnetic field that is directed out of the page as shown in figure

26, which also shows the paths taken by the two particles as they move through the field. The particles are not

subject to any other forces or fields. Which one of the following statements is correct? A. Both particles are negatively charged.

B. Both particles are positively charged.

C. The particles may both be neutral.

D. Particle 1 is positive, but particle 2 is negative.

E. Particle 1 is negative, but particle 2 is positive.

19. A wire of length L carries a current I and is bent in the form of a circle. What is the magnitude of its

magnetic moment?

A. IL2

B. 2IL

/4π 2

C. IL

/π 2

D. IL

/π 2

E. 4πIL

/2π

20. Which of the following statements is true?

2

A. A magnetic field alone cannot change the speed of a moving charged particle.

B. In a uniform magnetic field, faster protons make circles in shorter times than

slower protons.

C. The direction of magnetic forces is the same for a proton and electron moving in

the same direction.

D. In a uniform magnetic field, there is always non-zero force on a moving charge

particle.

E. A magnetic field alone cannot accelerate a moving charged particle.

21. An electron is traveling in the positive x direction. A uniform electric field E is in the negative y direction

as shown in figure 31. The magnetic field that will make the electron move in a straight line has a direction A. into the page

B. in the negative y direction

C. in the positive y direction

D. out of the page

E. in the negative x direction

22. Figure 32 shows the path of an electron that passes through two regions containing uniform magnetic

fields B1 and B2

A. B

. Its path in each region is a half circle. Which of the following statements is CORRECT? 1

B. B

has a larger magnitude.

1

C. The magnitudes of the two fields are equal.

has a smaller magnitude.

D. The two fields point in the same direction.

E. The electron spends the same time in both fields.


Figure 1 Figure 2

Figure 3

Figure 4 Figure 5 Figure 6

Figure 7

Figure 8 Figure 9 Figure 10

Figure 11

Figure 12 Figure 13

Figure 14


Figure 15 Figure 16

Figure 17

Figure 18

Figure 19

Figure 20 Figure 21

Figure 22

Figure 23 Figure 24

Figure 25


Figure 26 Figure 27

Figure 28

L

2 L

45 °

B 45 °

45 °

Ig

fI

Figure 29 Figure 30

Figure 31

Figure 32

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Chapter28.Magnetic