Calculate the magnetic field at the center of a square loop of side 10 cm carrying a current of 5A.

Problem statement: Calculate the magnetic field at the center of a square loop of side 10 cm carrying a current of 5A.

Solution:

Given:
Square loop’s side: a= 10 cm = 0.1 m
current I = 5 A
The magnetic field at the center of this square: B =?

The formula of the magnetic field B at the center of a square loop of side a, carrying a current I is as follows:
B=8√2[(μ₀ I)/(4πa)] [ see the derivation of the magnetic field B at the center of a square loop]

Hence, B = 8√2[(μ₀ I)/(4πa)] = 8√2[(4π x 10^-7 x 5)/(4π x 0.1)] = 4√2×10^-5 T = 5.66×10^-5 T
=>B = 5.66×10^-5 T