JEE Main · 2021 · 27 Jul 2021 · Shift 2 · Magnetic Effects of Current

Figure A and B show long straight wires of circular cross - section ( a and b with

a < b

), carrying current I which is uniformly distributed across the cross - section. The magnitude of magnetic field

B

varies with radius

r

and can be represented as :

Answer: (A)

Solution

Ampere's law on a circle of radius

r

coaxial with a wire of radius

R

carrying current

I

spread uniformly over the cross-section gives

B = \frac{μ _{0} I r}{2 π R ^{2}} (r < R), B = \frac{μ _{0} I}{2 π r} (r > R)

Inside the wire the field grows linearly with slope

\frac{μ _{0} I}{2 π R ^{2}}

and reaches its largest value

\frac{μ _{0} I}{2 π R}

at the surface; both the slope and the peak are larger for the thinner wire. Since

a < b

and the current is the same, the curve for the wire of radius

a

rises more steeply, peaks at the smaller radius and peaks higher, while the curve for radius

b

rises more gently, peaks at the larger radius and peaks lower. Beyond each surface the field falls off as

1/ r

. The graph in which the steeper, earlier and taller peak belongs to

a

and the gentler, later and shorter peak belongs to

b

represents the variation.

JEE Main · 2021 · 27 Jul 2021 · Shift 2 · Single correct option