PHYS102 Previous Exam Problems CHAPTER Magnetic …

Dr. M. F. Al-Kuhaili – PHYS 102 – Chapter 29 Page 1

PHYS102 Previous Exam Problems –

CHAPTER

29 Magnetic Fields Due to Currents

Calculating the magnetic field Forces between currents Ampere’s law Solenoids

1. Two long straight wires penetrate the plane of the paper at two vertices of an equilateral triangle, as shown

in figure 1. They each carry a 2.0-A current, out of the page. What is the magnitude of the magnetic field at the

third vertex (P)? (Ans: 1.7×10−5 T)

2. A long, coaxial cable, shown in cross-section in figure 3, is made of two conductors that share a common

central axis, labeled C. The current in the inner conductor is 2.0 A directed into the page and that in the outer

conductor is 2.5 A directed out of the page. The distance from point C to B is 0.0030 m. What are the magnitude

and direction of the magnetic field at point B? (Ans: 3.3×10–5 T, counterclockwise)

3. Solenoid 2 has twice the radius and six times the number of turns per unit length as solenoid 1. Find the

ratio of the magnetic field in the interior of solenoid 2 to that in the interior of solenoid 1, if the two solenoids

carry the same current. (Ans: 6)

4. In figure 4, two long parallel straight wires, at a separation d = 20.0 cm, carry currents i1 = 3.61 mA and

i2 = 3.00 mA, out of the page. At what distance from the origin on the x axis is the net magnetic field due to the

currents equal zero? (Ans: 11 cm)

5. What are the strength and direction of the magnetic field at point P in figure 5, at the center of the circular

arcs, if the current in the loop is 5.0 A? (Ans: 79 μT, into the page)

6. A long solid cylindrical wire, of radius R = 2.0 cm carries a uniform current of 1.9 A. Find the magnetic

field strength at a distance of 1.0 cm from the center of the wire. (Ans: 9.5 μT)

7. We wish to generate a 0.10-T uniform magnetic field near the center of a 10-cm long ideal solenoid. What

is the minimum number of turns needed, if the wire can carry a maximum current of 10 A? (Ans: 800)

8. What is the magnetic field at the center of the loop in figure 8? (Ans: 2.1×10-4 T, into the page)

9. What is the net force per unit length on the upper wire (# 1) in figure 9? (Ans: 1.0×10-4 N/m, upward)

10. A very long wire carries a current I = 0.5 A directed along the negative x axis. Part of the wire is bent into

a circular section of radius R = 2.5 cm, as shown in figure 12. What is magnetic field at point C?

(Ans: 16.6 μT, into the page)

11. An ideal solenoid that is 100 cm long has a diameter of 5.0 cm and a winding of 1000 turns, and carries a

current of 5.0 A. Calculate the magnitude of the magnetic field inside the solenoid. (Ans: 6.3 mT)

12. The radius R of a long current-carrying wire is 4.2 cm. If the magnetic field at r1 = 3.0 cm is equal to four

times the magnetic field at r2, where r2 > R, calculate the distance r2. (Ans: 23.5 cm)


13. Figure 13 shows a hollow cylindrical conductor, of inner radius a = 3.0 mm and outer radius b = 5.0 mm,

that carries a current of 2.0 A parallel to its axis. The current is uniformly distributed over the cross section of

the conductor. Find the magnitude of the magnetic field at a point that is 2.0 mm from the axis of the conductor.

(Ans: zero)

14. Two long straight wires are parallel and carry currents in opposite directions. The currents are 8.0 and

12A, and the wires are separated by 0.40 cm. What is the magnitude of the magnetic field at a point midway

between the wires? (Ans: 20×10−4 T)

15. Suppose that the identical currents I in figure 15 are all out of the page. What is the magnitude of the force

per unit length on the wire at the origin? [take I = 10.0 A, and a = 10-4 m] (Ans: 0.28 N/m)

16. What is the magnitude of the magnetic field at point P due to the current carrying wire shown in figure 16,

if I = 2.0 A, a = 20 cm and b = 2a? (Ans: 0.8 μT)

17. Two long wires parallel to the x-axis carry currents I1 and I2, as shown in figure 17. If I1 = 5 A, what is the

magnitude and direction of I2 if the net magnetic field at the origin is 0.35 μT, and directed out the page.

(Ans: 1 A to the left)

18. Figure 18 shows four wires carrying currents I1, I2, I3, and I4. What is the value of the integral sB d. for

the Amperian loop shown in the figure? (Ans: 3.8×10-6 T.m)

19. Figure 19 shows three parallel wires carrying currents I1 = 2 A, I2 = 6 A, and I3. The spacing between

adjacent wires is 1 cm. Calculate the value of I3 such that the magnitude of the net force per unit length at the

third wire is 0.25×10-3 N/m. (Ans: 2.5 A)

20. A cylindrical ring with inner radius R1 = 2.0 mm and outer radius R2 = 5.0 mm, carries a constant current

of 8.0 A along its length. What is the current density? (Ans: 1.2×105 A/m2)

21. Figure 21 shows two concentric, circular wire loops, of radii r1 = 15 cm and r2 = 30 cm, that are located in

the xy plane. The inner loop carries a current of 8.0 A in the clockwise direction, and the outer loop carries a

current of 10.0 A in the counter clockwise direction. Find the net magnetic field at the center.

(Ans: 12.6×10-6 T, directed into the page)

22. How strong is the magnetic field at a distance of 10.0 cm from a long straight wire, of radius 3.0 cm

carrying a current of 5.0 A? (Ans: 1.0×10-5 T)

23. Three long parallel wires are arranged as shown in figure 22. Wires 1 and 3 each carries a current of 5.0

A in the directions shown. If the net magnetic force on wire 3 is zero, what is the magnitude and direction of the

current in wire 2? (Ans: 2.5 A, downward)

24. A segment of wire is formed into the shape shown in figure 23, and carries a current I = 1.0 A. What is the

magnitude of the resulting magnetic field at point P if R = 10 cm? (Ans: 5.5 μT, into the page)

25. A solenoid has length L = 2.0 m and diameter d = 4.0 cm, and it carries a current I = 6.0 A. It consists of

seven closely-packed layers, each with 90 turns along length L. What is B at its center? (Ans: 2.4×10-3 T)

26. Two infinite parallel wires are separated by 2.5 cm and carry currents of 10 A and 12 A in the same

direction. What is the force per unit length on each wire? (Ans: 9.6×10-4 N/m, attractive)

27. Four long conducting wires are parallel to each other. Their cross sections form the corners of a square of

side a = 15 cm. The directions of the currents are as shown in figure 24. The magnitude of the current in each

wire is 15 A. What is the magnitude of the magnetic field at the center of the square? (Ans: zero)


28. Two long parallel wires, D and B, are separated by 2.0 cm. The current in D is three times the current in

B. If the magnitude of the force on a 2.0-m length of one of the wires is equal to 60 μN, find the current in B.

(Ans: 1.0 A)

29. Consider an infinitely long straight wire carrying a current I. If the magnetic field at r1 = 2.5 mm inside

the wire and at r2 = 10 mm outside the wire are equal, what is the radius of the wire? (Ans: 5.0 mm)

30. Three long parallel wires, shown in figure 26, are in the xy plane. Each wire carries a current of 3.0 A. The

separation between adjacent wires is d = 8.0 cm. What is the magnitude of the net force per meter exerted on the

central wire by the other two wires? (Ans: 4.5×10-5 N/m)

31. A long solid cylindrical conductor of radius R = 4.0 mm carries a current I parallel to its axis. The current

density in the wire is 2.0×104 A/m2. Determine the magnitude of the magnetic field at a point that is 5.0 mm

from the axis of the conductor. (Ans: 40 μT)

32. A solenoid is 3.00 m long and has a circumference of 9.40 cm. It carries a current of 12.0 A. The magnetic

field inside the solenoid is 25.0×10-3 T. What is the length of the wire forming the solenoid? (Ans: 468 m)

33. In the loop shown in figure 28, a = 5.0 cm, b = 10 cm, and i = 1.0 A. What is the magnetic field at point P,

which is the center of the two circular arcs? (Ans: 9.4×10-6 T, into the page)

34. Figure 30 shows two current segments. The lower segment carries current I1 = 0.50 A, and includes a

circular arc of radius 5.0 cm. The upper segment carries current I2 = 0.90 A, and includes a circular arc of radius

4.0 cm. Both arcs are centered at point P. What is magnitude of the magnetic field at P? (Ans: 1.6 μT)

35. In figure 32, a wire forms a quarter of a circle of radius R = 3.14 m and two straight segments of length

5.5 m. The wire carries a current of 20.0 A. What is the magnitude and direction of magnetic field at the center?

(Ans: 1.00 μT, into the page)

36. In figure 34, the current in both very long wires is i = 5.00 A and R = 2.00 cm. What is the magnitude of

the magnetic field at point P, at the center of the semicircle shown? (Ans: 28.5 μT, into the page)

37. Figure 35 shows, in cross section, two wires that are parallel, straight, and very long. The first wire,

located at (0, 5.0) cm, carries a current of 6.0 A into the page, and the other wire, located at (–3.0, 4.0) cm,

carries a current of 7.5 A out of the page. What magnetic field do these two wires produce at the origin O?

(Ans: 18 j μT)

38. Figure 36 shows a current-carrying loop. The three circular arcs have radii 1.0, 2.0, and 3.0 cm, and

subtend angles 45o, 90o, and 180o, respectively. If the smallest arc alone produces a magnetic field of magnitude

12 μT at point O, what is the magnitude of the total magnetic field produced by the whole loop at point O?

(Ans: 16 μT)

39. Figure 38 shows a cross section of three parallel wires, each carrying a current of 12 A. The currents in

wires A and C are out of the page, while that in wire B is into the page. If the distance R = 4.0 mm, what is the

magnitude of the magnetic force on a 3.0-m length of wire B? (Ans: 11 mN)

40. Figure 41 shows two long, thin wires that carry currents in the positive z direction. Both wires are parallel

to the z axis. The 50-A wire is in the xz plane and is 5.0 m from the z axis. The 40-A wire is in the yz plane and

is 4.0 m from the z axis. What is the magnitude of the magnetic field at the origin? (Ans: 2.8 μT)

41. A long, straight, hollow conductor, that has an inner radius of 1.0 mm and an outer radius of 3.0 mm,

carries a current of 15 A uniformly distributed over its cross section. What is the magnitude of the magnetic

field at a distance of 4.0 mm from the axis of the wire? (Ans: 0.75 mT)


42. A long solenoid has 1000 turns/m and carries current I. An electron moves within the solenoid in a circle

of radius 2.30 cm perpendicular to the solenoid axis. The speed of the electron is 1.35×107 m/s. What is the

current in the solenoid? (Ans: 2.66 A)

43. Five long, straight, insulated wires are closely bound together to form a small cable of diameter 1.0 cm.

Currents carried by the wires are I1 = 20 A, I2 = -6 A, I3 = 12 A, I4 = -7 A, and I5 = 18 A (negative currents are

opposite in direction to the positive). Find the magnitude of the magnetic field at a distance 10 cm from the

cable. (Ans: 74 μT)

44. A copper wire is of total length 1.0 m. You want to make N-turn circular current loop, using the entire

wire, that generates a 1.0-mT magnetic field at the center of the coil when the current is 1.0 A. What will be the

diameter of your coil? (Ans: 0.020 m)

45. Two long straight current-carrying parallel wires cross the x-axis and carry currents I and 3I in the same

direction, as shown in figure 43. At what value of x is the net magnetic field zero? (Ans: 1.0 cm)

46. Two long straight current-carrying parallel wires cross the x axis and carry currents I and 3I in the

directions shown in figure 44. At what value of x is the net magnetic field zero? (Ans: 0)

47. Figure 45 shows two long, parallel current-carrying wires. These wires carry equal currents I1 = I2 = 20 A,

and are separated by a distance d = 0.50 m. Calculate the magnetic field at point P. (Ans: +8.0 j μT)

48. A cylindrical infinitely long wire has a radius of 4.0 mm. What current will produce a maximum magnetic

field of 0.50 mT? (Ans: 10 A)

49. The radius of a coil of wire with N turns is r = 0.22 m. A clockwise current of Icoil = 2.0 A flows in the

coil, as shown in figure 47. A long, straight wire carrying a current Iwire = 31 A toward the left is located at a

distance d = 0.05 m from the edge of the coil. The magnetic field at the center of the coil is zero. Determine N,

the number of turns. (Ans: 4)

50. Figure 48 shows a wire consisting of concentric circular arcs of radii r, 2r and 3r, where r = 1.0 cm. The

wire carries a current i = 1.0 A. Calculate the magnetic field at point C. (Ans: 13 μT, out of the page)

51. Two long straight wires enter a room through a door. One carries a current of 3.0 A into the room while

the other carries a current of 5.0 A out of the room. What is the magnitude of the path integral sB d. around the

door frame? (Ans: 2.5 × 10-6 T · m)

52. In figure 49, a closed loop carries current i = 0.20 A. The loop consists of two straight wires and two

concentric circular arcs of radii R1 = 2.0 m and R2 = 4.0 m. What is the magnetic field at the center P?

(Ans: 2.4 × 10-8 T into the page)

53. Figure 50 shows three long parallel wires at the vertices of an equilateral triangle of side a = 10 cm, and

carrying the same current I = 5.0 A. The currents in wires 1 and 2 are out of the page, while in wire 3 the current

is into the page. Calculate the net magnetic force per unit length on wire 3 due to wires 1 and 2.

(Ans: +8.7 × 10-5 j N/m)

54. Two infinitely long wires carry currents in opposite directions, as shown in figure 51. The current in each

wire is 5.0 A, and the distance d = 1.0 m. What is the net magnetic field at point P? (Ans: 0.50 μT, to the left)

55. A long, solid, cylindrical wire carries a uniformly distributed current. If the radius of the wire is 3.5 mm,

and the magnitude of the current density is 1.5 A/cm2, what is the magnitude of the magnetic field at a distance

of 2.5 mm from the axis of the wire? (Ans: 24 μT)


56. Figure 55 shows two wires each carrying a current in the direction indicated in the figure. Wire 1, which

consists of a circular arc of radius R and two radial lengths, carries a current I1= 1.5 A. Wire 2 is long and

straight; carries a current I2= 0.4 A and is at a distance R/2 from the center of the arc. For what value of arc

angle φ the net magnetic field B at point P due to the two currents is zero? (Ans: 61o)

57. Two long wires are oriented so that they are perpendicular to each other, as shown in figure 57. What is

the magnitude of the magnetic field at a point midway between them if the top one carries a current of 20.0 A,

and the bottom one carries a current of 5.00 A? (Ans: 4.12 × 10-5 )

58. The value of the line integral sB d. around the closed path in figure 58 is 1.4 × 10-5 T.m. What are the

direction and magnitude of I3? (Ans: 19 A, into the page)

59. Three long wires 1,2 and 3 are parallel to a z axis, and each carries a current of 2.0 A in the positive z

direction (out of page). Their point of intersection with the xy plane form an equilateral triangle with sides of 50

cm, as shown in figure 60. A fourth wire (wire 4) passes through the midpoint of the base of the triangle and is

parallel to the other three wires. If the net magnetic force on wire 1 is zero, what is the magnitude and direction

of the current in wire 4? (Ans: 3.0 A, into the page)

60. The loop shown in figure 61 consists of two semicircles 1 and 2 (with the same center) and two radial

lengths. The semicircle 1 lies in the xy plane and has a radius of 10.0 cm, and the semicircle 2 lies in the xz

plane and has a radius of 4.00 cm. If the current i in the loop is 0.500 A, what is magnitude of the magnetic field

at point P, located at the center of the loops? (Ans: 4.23 μT)

61. Figure 62 shows three long, parallel, current-carrying wires carrying equal magnitude of current. The

directions of currents I1 and I3 are out of page. The arrow labeled F represents the magnetic force per unit length

acting on current I3 due to the other two wires and is given by F = (− 0.220 i − 0.220 j ) (N/m) . What are the

magnitude and direction of the current I2, if the distance d = 1.00 mm? (Ans: 33.2 A, into the page)


A B C D E Conceptual Problems 1. Four long straight wires, carrying equal currents out of the page, are placed at the corners of a square, as

shown in figure 2. What is the net magnetic force on wire P?

A. East

B. North

C. South

D. West

E. South west

2. Figure 6 shows three wires that are perpendicular to the page. The currents are all equal, two being out of

page and one being into the page. Rank the wires according to the magnitudes of the magnetic forces on them,

greatest first.

A. 1 and 3 tie, then 2

B. 2, then 1 and 3 tie

C. 1, then 2, then 3

D. 2 and 3 tie, then 1

E. 3, then 2, then 1

3. Two long straight, parallel wires are 3.0 cm apart. They carry currents I1 = 3.0 A and I2 = 5.0 A in opposite

directions, as shown in the figure 7. At what point, beside infinity, could the magnetic field be zero?

A. A

B. B

C. C

D. D

E. E

4. Figure 10 shows four wires carrying equal current and four Amperian loops. Rank the loops according to

the magnitude of sB d. along each, greatest first

A. c, b and d tie, then a

B. a, b and a tie, then c

C. c, a, b, d

D. c, d, a, b

E. a, b, c, d

5. An infinitely long wire has a charge density λ per unit length. The wire moves along its axis with velocity v.

The ratio of the magnetic field to the eclectic field at a point r from the wire is:

A. independent of r

B. directly proportional to λ C. proportional to r

D. inversely proportional to r

E. inversely proportional to r2

6. Four long straight wires carry equal currents into the page, as shown in the figure 11. What is the direction

of the net magnetic force exerted on wire A by the other three wires?

A. East

B. North

C. South

D. West

E. zero


7. Figure 14 shows a small positive charge q moving toward a long current-carrying wire. Which of the

arrows labeled A to D correctly represents the direction of the magnetic force on the charge?

A. C

B. A

C. B

D. D

E. The force points in a direction perpendicular to the plane of the figure.

8. Figure 20 shows three arrangements of circular loops, centered on vertical axes and carrying identical

currents in the directions indicated. Rank the arrangements according to the magnitudes of the magnetic fields at

the midpoints between the loops on the central axes, maximum to minimum.

A. 1, 3, 2

B. 3, 2, 1

C. 3, 1, 2

D. 2, 3, 1

E. 2, 1, 3

9. Two long parallel straight wires carry equal currents in opposite directions. At a point midway between the

wires, the magnetic field they produce is

A. non-zero and perpendicular to the plane of the two wires.

B. zero.

C. none of the answers.

D. non-zero and parallel to the wires.

E. non-zero and along a line connecting the wires.

10. An electron is moving along the axis of a solenoid carrying a current. Which of the following is a

correct statement about the magnetic force acting on the electron?

A. No force acts

B. The force acts radially inward.

C. The force acts radially outward.

D. The force acts in the direction of motion

E. The force acts opposite to the direction of motion

11. Figure 25 shows four circular loops that are concentric with a wire whose current is directed out of the

page. The current is uniform across the cross section of the wire. Rank the loops according to the magnitude of

the enclosed current, greatest first. [Loops a and b are inside the wires. Loops c and d are outside]

A. d = c > b > a.

B. d > c > b > a.

C. a > c > b > d.

D. a > c > b > d.

E. a = b > c > d.

12. A proton is moving along the axis of a solenoid carrying a current. Which of the following statement is

correct about the magnetic force acting on the proton?

A. No force acts.

B. The force acts radially inwards.

C. The force acts radially outwards.

D. The force acts in the direction of motion.

E. The force acts in the opposite direction of motion.


13. Figure 27 shows two wires carrying anti-parallel currents. If i2 is greater than i1, the point at which the

resultant magnetic field of the two wires will be zero is located in the region (regions):

A. I

B. II and III

B. I

C. I and III

D. II

E. III

14. An infinitely long wire carrying current I is bent at a right angle as shown in figure 29. What is the

magnetic field at point P that is a distance y from the corner of the wire?

15. Wires A, B, and C carry equal currents in the directions shown in Figure 31. What is the direction of the

net magnetic force on wire C due to wires A and B?

A. Negative y direction

B. Positive x direction

C. Negative x direction

D. Positive y direction

E. Positive z direction

16. Three long straight wires are perpendicular to the page, and are placed at three corners of a square of edge

length a = 20 cm, as shown in figure 33. Wires number 1, 2 and 3 each carries a 1.0-A current out of the page.

What is the direction of the net force on wire number 1 due to wires number 2 and 3?

A. Towards point P

B. Away from point P

C. Towards wire number 2

D. Away from wire number 2

E. Towards wire number 3

17. Three wires carrying currents of magnitudes i1, i2 and i3 in the directions shown in figure 37. Which one of

the following integrals is correct?


18. In figure 39, two long straight wires are perpendicular to the page. Each carries a current of 25.0 A

directed out of the page. In unit vector notation, what is the net magnetic force per unit length on the wire at the

origin?

A. 6.25×10-4 ( i + j ) N/m

B. 1.84×10-4 ( i - j ) N/m

C. 6.25×10-4 (- i - j ) N/m

D. 1.84×10-4 (- i - j ) N/m

E. 2.16×10-4 (- i + j ) N/m

19. A cylindrical wire of radius R carries current I that is uniformly distributed across its cross-section. Find

the magnitude of the magnetic field inside the wire at r < R from the axis.

A. μ0Ir/(2πR2)

B. μ0I/(2πR)

C. μ0I/(2πr)

D. μ0IR2/(2πr2)

E. μ0I/(4πr)

20. Two long parallel wires, a distance d apart, carry currents of I and 5I in the same direction. Locate the

point r, from I, at which their magnetic fields cancel each other.

A. r=d/6

B. r=d/2

C. r=2d

D. r=3d/2

E. r=d/4

21. Two parallel wires, carrying equal currents of 10 A, attract each other with a force F. If both currents are

doubled, and the distance between them is reduced by 50%, what will be the new force?

A. 8F

B. 16F

C. 4F

D. F

E. F/4

22. Figure 40 shows the cross section of a long solid wire carrying a uniform current i. The radius of the wire

is R. What is the value of the integral sB d. over the circular closed path of radius r shown in the figure?

A. μoi(r/R)2

B. μoir/R2

C. μoiR/r

D. μoiR2/r

E. μoi

23. Two long wires are parallel to the z-axis as shown in figure 42. Find the resultant magnetic field at the

origin, given that the wires carry equal current I and moves in the same direction. [Take I = 1.0 A, and a =0.5 m]

A. Zero.

B. 8.0×10-4 T, In the negative x-direction.

C. 3.2×10-3 T, In the positive z-direction.

D. 3.2×10-4 T, In the positive z-direction.

E. 8.0×10-7 T, In the positive x-direction.


24. Three current-carrying wires A, B and C are placed as shown in figure 46. All currents have the same

value. Wire C has a current that flows into the page. The three wires are at equal distances from the origin. If

the net magnetic force on wire C due to wires A and B is in the positive y direction, then

A. Wires A and B must have currents flowing into the page.

B. Wires A and B must have currents flowing out of the page.

C. Wire A has a current flowing out of the page,

and wire B has a current flowing into the page.

D. Wire A has a current flowing into the page,

and wire B has a current flowing out of the page.

E. The net magnetic force can never be along the positive y axis.

25. Figure 52 shows a snapshot of the velocity vectors of five electrons near a wire carrying current i. The five

velocities have the same magnitude. Which electron experiences the largest magnetic force?

A. 1

B. 2

C. 3

D. 4

E. 5

26. Two long wires are placed in the xy plane, as shown in figure 53. Each wire carries a current of 1.5 A,

directed out of the page. If the distance d = 3.0 m, what is the net magnetic field due to these wires at the origin?

A. (+0.10 i – 0.10 j ) (μT)

B. (+0.10 i + 0.10 j ) (μT)

C. (–0.10 i – 0.10 j ) (μT)

D. (–0.10 i + 0.10 j ) (μT)

E. zero

27. In figure 54, two infinitely long wires carry currents i. Each follows a 90o arc on the circumference of the

same circle of radius R. What is the magnitude of the net magnetic field at the center of the circle (point C)?

A. Rio

πμ2

B. Rio

πμ

C. Rio

πμ4

D. Ri

Ri oo

162

μ+π

μ

E. Ri

Ri oo

16

μ+πμ

28. Figure 56 shows three circuits consisting of straight radial lengths and concentric circular arcs (either half-

or quarter-circles of radii r or 2r). The circuits carry the same current in the indicated direction. Rank the circuits

according to the magnitude of the magnetic field produced at the center of curvature (the dot), greatest first.

A) B2, B1, B3

B) B1, B2, B3

C) B3, B2, B1

D) B2, B3, B1

E) B1, B3, B2


29. Figure 59 shows four different sets of wires that cross each other without touching. The magnitude of the

current is the same in all four cases, and the directions of current flow are as indicated. For which configuration

will the magnetic field at the center of the square formed by the wires be equal to zero?

A) 3

B) 1

C) 2

D) 4

E) The filed is equal to zero in all four cases


Figure 1 Figure 2 Figure 3




Figure 13 Figure 14 Figure 15 Figure 16










Figure 38 Figure 39





Figure 49 Figure 50 Figure 51 Figure 52


Figure 56 Figure 57


Figure 58 Figure 59


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PHYS102 Previous Exam Problems CHAPTER Magnetic …