Question

Four wires running through the corners of a square with sides of length 16.166 cm carry equal currents, 3.684 A. Calculate the magnetic field at the center of the square.

Answer 1

For practical reasons, we can consider each side of the square as an infinite wire. This can be seen on the following drawing:

This way, the field on the center will be the sum of the contribution of each wire. We can calculate the contribution of a single wire as:

`B=(\mu_0i)/(2\pi d)=(4\pi *10^(-7)*3.684)/(2\pi((16.166*10^(-2))/(2)))=9.115*10^(-6)T`

Then, the total field will be this, multiplied by the number of wires:

`B_t=4*9.115*10^(-6)=36.46\mu T`

Then, the resulting field will be Bt=36.46uT