Question

You have a 1.6 m long copper wire. You want to make an N-turn current loop that generates a 2.5 mT magnetic field at the center when the current is 1.9 A . You must use the entire wire. What will be the diameter of your coil?

Answer 1

length l = 1.6m

magnetic field B = 2.5 x 10^-3 T

current i = 1.9A

but B = u₀ni/D

hence number of turns n = B.D /u₀ i _{...........................}(1)

here length = number of turns x circumference

1.6 = n x pi.D

hence n = 1.6 / pi. D....................(2)

from 1 and 2

  B.D /u₀ i _. = 1.6 / pi. D

D² = (1.6 x u₀ i) / B pi

= (1.6 x 4pi. x 10^-7 x 1.9)/ 2.5 x 10^-3 pi

= 12.16 x 10^-7 / 2.5 x 10^-3

= 4.9 x 10^-4

hence diameter D = sq.root of (4.9 x 10^-4)

= 2.205 cm

= 0.02205 m