Question

Two identical wires A and B have the same length $L$ and carry the same current $I$. Wire A is bent into a circle of radius $R$ and wire B is bent to form a square of side $a$. If $B_1$ and $B_2$ are the values of magnetic induction at the centre of the square respectively, then the ratio $\frac{B_1{B_2}$ is}

• A. $\frac{\pi}{8}$
• B. $\frac{\pi}{8\sqrt{2}}$
• C. $\frac{\pi}{16}$
• D. $\frac{\pi}{6}$

Hint:

The magnetic field produced by a loop is inversely proportional to its radius, and the magnetic field produced by a square loop is a bit more complex.

Answer 1

The Correct Option is B

The magnetic field at the center of a loop is given by: \[ B = \frac{\mu_0 I}{2R} \] For the square, the magnetic field at the center is: \[ B = \frac{\mu_0 I}{4a} \] Thus, the ratio is: \[ \frac{B_1}{B_2} = \frac{\pi}{8\sqrt{2}} \]