JEE Main · 2022 · 25 Jun 2022 · Shift 1 · Magnetic Effects of Current

WhatsApp Email

A long straight wire with a circular crosssection having radius R , is carrying a steady current I. The current I is uniformly distributed across this cross-section. Then the variation of magnetic field due to current I with distance

r (r < R)

from its centre will be :-

(A) $B \propto r^{2}$
(B) $B \propto r$ ✓ Correct
(C) $B \propto \frac{1}{r ^{2}}$
(D) $B \propto \frac{1}{r}$

Answer: (B)

Solution

Using Ampere's circuital law for a circular path of radius

r < R

inside the wire:

B \cdot 2 π r = μ_{0} I_{enclosed}

Since current is uniformly distributed, the enclosed current is:

I_{enclosed} = I \cdot \frac{π r ^{2}}{π R ^{2}} = I \frac{r ^{2}}{R ^{2}}

Substituting:

B \cdot 2 π r = μ_{0} I \frac{r ^{2}}{R ^{2}}

B = \frac{μ _{0} I r}{2 π R ^{2}}

Therefore:

B \propto r

Answer: (B)

JEE Main · 2022 · 25 Jun 2022 · Shift 1 · Single correct option

Practise more: all JEE Main PYQs on Magnetic Effects of Current →

JEE Main · 2022 · 25 Jun 2022 · Shift 1 · Magnetic Effects of Current

Solution

More JEE Main questions on Magnetic Effects of Current