JEE Main · 2020 · 09 Jan 2020 · Shift 1 · Magnetic Effects of Current

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A long, straight wire of radius a carries a current distributed uniformly over its crosssection. The ratio of the magnetic fields due to the wire at distance

\frac{a}{3}

and 2 a , respectively from the axis of the wire is:

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

Answer: (A)

Solution

Inside a uniformly carrying wire the field grows linearly,

B = \frac{μ _{0} i r}{2 π a ^{2}}

, so at

r = \frac{a}{3}

it equals

\frac{μ _{0} i}{6 π a}

. Outside the wire the field falls off as

\frac{μ _{0} i}{2 π r}

, so at

r = 2 a

it equals

\frac{μ _{0} i}{4 π a}

. The ratio of the first to the second is

\frac{1/6}{1/4} = \frac{4}{6} = \frac{2}{3}

JEE Main · 2020 · 09 Jan 2020 · Shift 1 · Single correct option

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