JEE Main · 2025 · 28 Jan 2025 · Shift 2 · Magnetic Effects of Current

An infinite wire has a circular bend of radius a, and carrying a current

I

as shown in figure. The magnitude of magnetic field at the origin O of the arc is given by :

Answer: (B)

Solution

The wire consists of two semi-infinite straight segments joined by a circular arc of radius

a

, with the origin O at the centre of the arc.

**Straight segment ending at O (perpendicular distance

a

from O, extending to infinity on one side only):**

B_{1} = \frac{μ _{0} I}{4 π a}

**Circular arc subtending

\frac{3 π}{2}

radians (270°) at O:**
Field due to a full circular loop at its centre is

μ_{0} I /2 a

, so for a fraction

θ /2 π

of the loop,

B_{2} = \frac{μ _{0} I}{2 a} \times \frac{1}{2 π} \times \frac{3 π}{2} = \frac{μ _{0} I}{4 π a} \times \frac{3 π}{2}

Straight segment lying along the line through O (its extension passes through O):

B_{3} = 0

All three contributions point in the same direction (into the page), so they add:

B = B_{1} + B_{2} + B_{3} = \frac{μ _{0} I}{4 π a} + \frac{μ _{0} I}{4 π a} \times \frac{3 π}{2} = \frac{μ _{0} I}{4 π a} [\frac{3 π}{2} + 1]

JEE Main · 2025 · 28 Jan 2025 · Shift 2 · Single correct option