Question

Four wires running through the corners of a square with sides of length 5.278 cm carry equal currents, 3.403 A. Calculate the magnetic field at the center of the square.

Answer 1

In order to calculate the magnetic field generated by each wire, we can use the formula below:

`B=(\mu_0)/(2\pi)\cdot(I)/(r)`

Where u0 is the permeability of free space: 4pi * 10^-7 T*m/A

The distance from one corner of the square to the center of the square is given by:

`r=(d)/(2)=(l√(2))/(2)=(0.05278\cdot1.4142)/(2)=0.0373\text{ m}`

Now, calculating the magnetic field generated by one wire, we have:

`\begin{gathered} B=(4\pi\cdot10^(-7))/(2\pi)\cdot(3.403)/(0.0373)\\ \\ B=2\cdot10^(-7)\cdot91.23\\ \\ B=1.8246\cdot10^(-5)\text{ T} \end{gathered}`

Since we have four wires at the same distance from the center of the square and with the same current, the magnitude of each magnetic field generated is the same, but we need to check the direction of each field: