Q 12-04-099JEE MainJEE Main 2024 (30 Jan, Shift 2)Medium
A current of $5\ \text{A}$ flows in a square loop of side $1\ \text{m}$ placed in air. The magnetic field at the centre of the loop is $X\sqrt2\times10^{-7}\ \text{T}$. The value of $X$ is ______.
Numerical value type. Enter your answer.
Answer: 40
For a square of side $a$, each side is at distance $a/2$ from the centre and subtends $45^\circ$ on either side:
$$B = 4\times\frac{\mu_0 I}{4\pi(a/2)}(\sin45^\circ + \sin45^\circ) = \frac{2\sqrt2\,\mu_0 I}{\pi a}$$
$$B = \frac{2\sqrt2\times4\pi\times10^{-7}\times5}{\pi\times1} = 40\sqrt2\times10^{-7}\ \text{T}$$
$X = 40$.
Solution by Sreeraj P, M.Sc Physics