Question

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

• A. independent of L
• B. proportional to $L^2$
• C. inversely proportional to L
• D. linearly proportional to L

Answer 1

Answer: (C)

inversely proportional to L

Answer 2

Magnetic field at the centre due to either arm $B_1= \frac {\mu _0}{4 \pi} \times \frac {i}{(L/2)}[sin \, 45^\circ +sin \, 45^\circ ]$ $= \frac {\mu _0}{4 \pi} \times \frac {2 \sqrt 2 i}{L}$ Field at centre due to the four arms of the square $B=4B_1= \frac {\mu _0}{\pi} \times \frac {2 \sqrt 2 i}{L}$ i.e., $, , , , , , , , B ?