9. A conducting rod with a square cross section (3.0cm * 3.0cm) carries a curren

Question

9. A conducting rod with a square cross section (3.0cm * 3.0cm) carries a current of 60A that is uniformly distributed across the cross section. What is the magnitude of the line integral B*ds around a square path (1.5cm * 1.5cm) if the path is centered on the center of the rod and lies in a plane perpendicular to the axis of the rod?

THE CORRECT ANSWER IS C.

What is the magnitude of the magnetic field at point P if a - 2R and b4R A) o 6R B) 3 3R 16R C) Hol 12R 16R 32R 9 A conducting rod with a square cross section (3.0 cm x 3.0 cm) carries a current of 60 A that is uniformly distributed across the cross section. What is the magnitude of the (line) integral f B ds around a square path (1.5 cm x 1.5 cm) ifth path is centered on the center of the rod and lies in a plane perpendicular to the axis of the rod? B) 75 HT m -CoA A :2.251- 19 HT m Ls E) Can not be determined with given information 3 8ds ids A 10. A hollow cylindrical (inner radius 1.0 mm, outer radius 3.0 mm) conductor carries a current of 80 A parallel to ts axis. This current is uniformly distributed over a cross section of the conductor. Determine the magnitude of the paagnetic field at a point that is 2.0 mm from the axis of the conductor A) 8.0 mT . B-4 3.0 mT C) 5.3 mT D) 16 mT E) 1.2 mT Page 3

Explanation / Answer

8. given a = 2R

b = 4R

now magnetic field at the center of a loop of radius r, and central angle phi is

B = k*phi*i/r

where phi is in radians

in the figure

the straight sections of the loop do not contribute to magnetic field at P as they are radially pointing towards the point

hence

Net fied out of the page is

B = k*phi*i/2R - k*phi*i/4R = k*phi*i/4R

now phi = pi/2

hence

B = pi*k*i/8R

k = mu/4*pi

hence

B = mu*i/32R

hence the answer is option E)

10. from ampere's law we know line integral around a current carrying wire is mu*i

hence B.dl = mu*i

i = 60 A

mu = 4*pi*10^-7

hence B.dl = 75.398 micro Tm

hence correct answer is option B

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