Question

A long current carrying hollow wire has an inner radius of 1.20 cm and an outer radius of 12.7 cm. The current in the wire is 6.00 A. Find the magnetic field at a distance 6.40 cm from the center of the wire.

Answer 1

Ri = inner radius = 1.20 cm = 0.012 m

Ro = outer radius = 12.7 cm = 0.127 m

A = Area = (Ro2 - Ri2) = (3.14)((0.127)2 - (0.012)2) = 0.0502 m2

i = current = 6 A

r = given distance where magnetic field is to be determined = 6.40 cm = 0.064 m

i' = current enclosed within the given radius

Current enclosed is given as

i' = i( (r2 - Ri2) )/A

i' = (6)( (3.14)(0.0642 - 0.0122) )/0.0502

i' = 1.5 A

Using ampere's law

B (2r) = i'

B (2 (3.14) (0.064)) = (12.56 x 10-7) (1.5)

B = 4.7 x 10-6 T