No figure A singlecoil loop of radius r 750 mm shown below

No figure

A single-coil loop of radius r = 7.50 mm, shown below, is formed in the middle of an infinitely long, thin, insulated straight wire carrying the current i = 20.0 mA. What is the magnitude of the magnetic field at the center of the loop?

Solution

B_line = mu₀ I / 2 pi r

B_loop = mu₀ I / 2 r

B_tot = [mu₀ I / 2 pi r] + [mu₀ I / 2 r]

B = mu₀ I / 2 r [1/pi + 1]

= [ 4 pi * 10^-7 * 20 * 10^-3 / 2 * 7.5 * 10^-3 ][1/pi + 1]

= 0.00000221 T = 2.21 * 10^-6 T