Question

A square conducting loop of side length $L$ carries a current $I$. The magnetic field at the center of the loop is

• A. independent of $L$
• B. proportional to $L$
• C. inversely proportional to $L$
• D. linearly proportional to $L$

Answer 1

Answer: (C)

inversely proportional to $L$

Magnetic field at the centre due to either arm

$B_1=\frac{{\mu }_0}{4\pi }\times \frac{I}{\left(L/2\right)}[\sin {45}^o+\sin {45}^o]$

$=\frac{{\mu }_0}{4\pi }\times \frac{2\sqrt{2}I}{\left(L\right)}$

Field at centre due to the four arms of the square

$=4B_1=4\times \frac{{\mu }_0}{4\pi }\times \frac{2\sqrt{2}I}{\left(L\right)}$

i.e., $B\propto \frac{1}{L}$