JEE Main · 2026 · 04 Apr 2026 · Shift 1 · Magnetic Effects of Current

An insulated wire is wound so that it forms a flat coil with N=200 turns. The radius of the innermost turn is

r_{1} = 3

cm, and of the outermost turn

r_{2} = 6

cm. If 20 mA current flow in it then the magnetic moment will be

α \times 1 0^{- 2}

A.m

^{2}

. The value of

α

is _____ .

Answer: (B)

Solution

Treating the

N

turns as spread uniformly in radius from

r_{1}

r_{2}

, the magnetic moment is

M = \frac{N I π}{r _{2} - r _{1}} \int_{r_{1}}^{r_{2}} r^{2} d r = \frac{N I π ( r _{2}^{3} - r _{1}^{3} )}{3 ( r _{2} - r _{1} )}

. Here

\frac{r _{2}^{3} - r _{1}^{3}}{r _{2} - r _{1}} = r_{2}^{2} + r_{1} r_{2} + r_{1}^{2} = 63 \times 1 0^{- 4}

^{2}

, so with

N = 200

and

I = 20 \times 1 0^{- 3}

M = \frac{200 ( 0.02 ) π ( 63 \times 1 0 ^{- 4} )}{3} = 2.64 \times 1 0^{- 2}

\cdot

^{2}

, giving

α = 2.64

JEE Main · 2026 · 04 Apr 2026 · Shift 1 · Single correct option