Two identical long current carrying wires are bent into the shapes… | JEE Main 2026 (2 Apr, Shift 1)

Q12JEE Main 2026 · 2 APR · SHIFT 1Medium

Magnetic Field of Straight Wires

Two identical long current carrying wires are bent into the shapes shown in the following figures. If the magnitude of magnetic fields at the centres P and Q of a semicircular arc are $B_1$ and $B_2$ respectively, then the ratio $\frac{B_1}{B_2}$ is ______.

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Answer: (a)

(I) Two semi-infinite wires, each $\frac{\mu_0 I}{4\pi r}$ , plus semicircle $\frac{\mu_0 I}{4r}$ , all into the page: $B_1 = \frac{\mu_0 I}{4\pi r}(\pi + 2)$ .
(II) The vertical wire's line passes through Q, so it gives zero. Top wire $\frac{\mu_0 I}{4\pi r}$ plus semicircle $\frac{\mu_0 I}{4r}$ : $B_2 = \frac{\mu_0 I}{4\pi r}(\pi + 1)$ .
$\frac{B_1}{B_2} = \frac{2 + \pi}{1 + \pi}$
So the answer is (a).

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