JEE Main · 2026 · 02 Apr 2026 · Shift 1 · Magnetic Effects of Current

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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 ____.

(A) $\frac{2 + π}{1 + π}$ ✓ Correct
(B) $\frac{1 + π}{1 - π}$
(C) $\frac{2 + π}{1 - π}$
(D) $\frac{1 + π}{2 - π}$

Answer: (A)

Solution

For the first configuration, the magnetic field at P is the sum of contributions from two straight segments and a semicircular arc:

B_{1} = \frac{μ _{0} I}{4 π r} \times 2 + \frac{μ _{0} I}{4 r} = \frac{μ _{0} I}{4 r} (\frac{2}{π} + 1)

. For the second configuration at Q:

B_{2} = \frac{μ _{0} I}{4 π r} + \frac{μ _{0} I}{4 r} = \frac{μ _{0} I}{4 r} (\frac{1}{π} + 1)

. Taking the ratio:

\frac{B _{1}}{B _{2}} = \frac{\frac{2}{π} + 1}{\frac{1}{π} + 1} = \frac{2 + π}{1 + π}

JEE Main · 2026 · 02 Apr 2026 · Shift 1 · Single correct option

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JEE Main · 2026 · 02 Apr 2026 · Shift 1 · Magnetic Effects of Current

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