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

The radius of the loop is 1.57 cm

Explanation:

Step 1:

Given data in the question  

Number of turns, n = 1

Current Magnitude i = 5.00 A

Now, let the Loop radius be r.

Step 2:

Therefore, the circuit current supplies the magnetic area in the middle

             $B=\frac{\mu_{0} i}{2 r}$

$0.2 \times 10^{-3}=\frac{4 \pi \times 10^{-7} \times 5}{2 r}$

$0.2 \times 10^{-3}=\frac{20 \pi \times 10^{-7}}{2 r}$

               $r=\frac{10 \pi \times 10^{-7}}{0.2 \times 10^{-3}}$

               $r=\frac{10 \times 3.14 \times 10^{-7}}{0.2 \times 10^{-3}}$

               $r=\frac{100 \times 3.14 \times 10^{-4}}{2} \mathrm{m}$

              $r=50 \times 3.14 \times 10^{-4} \mathrm{m}$

              $r=1.57 \times 10^{-2} \mathrm{m}$

                 $=1.57 \mathrm{cm}$