JEE Main · 2018 · 08 Apr 2018 · Offline · Magnetic Effects of Current

The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is

B_{1}

. When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is

B_{2}

. The ratio

\frac{B _{1}}{B _{2}}

is:

(A) $\frac{1}{2}$
(B)2
(C) $3$
(D) $2$ ✓ Correct

Answer: (D)

Solution

The loop's dipole moment is

m = I π r^{2}

, so at constant current doubling it means

π r^{'2} = 2 π r^{2}

, giving

r^{'} = 2 r

. The field at the centre of a current loop is

B = \frac{μ _{0} I}{2 r}

, which varies inversely with the radius, so

\frac{B _{1}}{B _{2}} = \frac{r ^{'}}{r} = 2

JEE Main · 2018 · 08 Apr 2018 · Offline · Single correct option

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