Question

A physics instructor is creating a demonstration that shows the direction of the field at the center of a current loop. He takes a cardboard form 25 cm in diameter and wraps 20 turns of wire around it in a tight loop. He wants the field at the loop’s center to be at least 10 times as large as the magnetic field of the earth, so that a compass will pivot convincingly to point in the direction of the field from the loop. How much current is needed to provide this field?

Answer 1

B = magnitude of earth's magnetic field = 25 x 10^-3 T = 0.025 T

B' = magnetic field at the center of loop = 10 B = 10 x 0.025 = 0.25 T

r = radius of the loop = diameter/2 = 25 cm/2 = 0.25/2 = 0.125 m

i = current in the loop

n = number of turns = 20

magnetic field at the center of loop is given as

B' = (/4) (2in/r)

0.25 = (10^-7) (2 (3.14) (20) i/0.125)

i = 2.5 x 10³ A