JEE Main · 2024 · 08 Apr 2024 · Shift 2 · Magnetic Effects of Current

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A long straight wire of radius a carries a steady current I. The current is uniformly distributed across its cross section. The ratio of the magnetic field at

\frac{a}{2}

and 2 a from axis of the wire is :

(A) $1 : 4$
(B) $4 : 1$
(C) $1 : 1$ ✓ Correct
(D) $3 : 4$

Answer: (C)

Solution

Current density is uniform,

J = \frac{I}{π a ^{2}}

.
Inside (

r < a

B = \frac{μ _{0} I r}{2 π a ^{2}}

. At

r = a /2

B_{1} = \frac{μ _{0} I}{4 π a}

.
Outside (

r > a

B = \frac{μ _{0} I}{2 π r}

. At

r = 2 a

B_{2} = \frac{μ _{0} I}{4 π a}

B_{1} : B_{2} = 1 : 1

JEE Main · 2024 · 08 Apr 2024 · Shift 2 · Single correct option

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