JEE Main · 2023 · 06 Apr 2023 · Shift 1 · Magnetic Effects of Current

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A long straight wire of circular cross-section (radius a) is carrying steady current I. The current I is uniformly distributed across this cross-section. The magnetic field is

(A)Zero in the region $r < a$ and inversely proportional to r in the region $r > a$
(B)Inversely proportional to r in the region $r < a$ and uniform throughout in the region $r > a$
(C)Directly proportional to r in the region $r < a$ and inversely proportional to r in the region $r > a$ ✓ Correct
(D)Uniform in the region $r < a$ and inversely proportional to distance r from the axis, in the region $r > a$

Answer: (C)

Solution

By Ampère's circuital law for a long straight wire of radius

a

carrying current

I

spread uniformly over its cross-section: at a point inside (

r < a

) the enclosed current is

I \frac{r ^{2}}{a ^{2}}

, giving

B = \frac{μ _{0} I r}{2 π a ^{2}}

, which is directly proportional to

r

. At a point outside (

r > a

) the whole current

I

is enclosed, giving

B = \frac{μ _{0} I}{2 π r}

, which is inversely proportional to

r

. The field thus grows linearly with

r

inside the wire and falls off as

1/ r

outside it.

JEE Main · 2023 · 06 Apr 2023 · Shift 1 · Single correct option

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JEE Main · 2023 · 06 Apr 2023 · Shift 1 · Magnetic Effects of Current

Solution

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