Question

A circular loop of one turn carries a current of 5.00 A. If the magnetic field B at the centre is 0.200 mT, find the radius of the loop.

Answer 1

Given:
No. of turns, n = 1
Magnitude of current, i = 5.00 A
Now, let the radius of the loop be r.
Thus, the magnetic field at the centre due to the current in the loop is given by
$B=\frac{{\mathrm{\mu }}_{0}i}{2r}$
$$\begin{gathered} \Rightarrow 0.2\times {10}^{-3}=\frac{4\mathrm{\pi }\times {10}^{-7}\times 5}{2r} \\ \Rightarrow r=1.57\times {10}^{-2}\mathrm{m}=1.57\mathrm{cm} \end{gathered}$$