Question

Four wires running through the corners of a square with sides of length 8.11 cm carry equal currents, 3.19 A. Calculate the magnetic field at the center of the square.

Answer 1

We will have the following:

First, we determine the distance:

$r=\frac{8.11\sqrt{2}}{2}cm\Rightarrow r=4.055\sqrt{2}cm$

Then, we will have that:

$\begin{gathered} B=\frac{(4\pi\ast10^{-7}Tm/A)(3.19A)}{2\pi(4.055\sqrt{2}cm\ast\frac{1m}{100cm})}\Rightarrow B=1.126427282...\ast10^{-5}T \\ \\ \Rightarrow B\approx1.13\ast10^{-5}T \end{gathered}$

So, the magnetic field is approximately 1.13*10^-5 T.