Verified Solution • 2025–26 Session moderate

QJEEM20Ph83a0: JEE Main 2020 Physics - Class 12 JEEM20Ph83a0 Solution: A long, straight wire of radius a carries a current distributed …

A long, straight wire of radius a carries a current distributed uniformly over its cross-section. The ratio of the magnetic fields due to the wire at distance a3{a \over 3} and 2 aa , respectively from the axis of the wire is :

Multiple Choice Options

  • A 2
  • B 12{1 \over 2}
  • C 32{3 \over 2}
  • D 23{2 \over 3}

Step-by-Step Verified Solution

JEE Main 2020 (Online) 9th January Morning Slot Physics - Magnetic Effect of Current Question 141 English Explanation

Let current density be J.

∴\therefore Applying Ampere's law. For point P

∮B.→dl→=μ0i\oint {\overrightarrow {B.} d\overrightarrow l } = {\mu _0}i

⇒\Rightarrow BP2 π\pi a3{a \over 3} = μ0Jπa29{\mu _0}J\pi {{{a^2}} \over 9} ...(1)

∴\therefore Applying Ampere's law. For point Q

BQ2 π\pi (2a){(2a)} = μ0Jπa2{\mu _0}J\pi {a^2} ...(2)

Dividing (1) by (2) we get

BP2πa3BQ4πa=μ0Jπa29μ0Jπa2{{{B_P}2\pi {a \over 3}} \over {{B_Q}4\pi a}} = {{{\mu _0}J\pi {{{a^2}} \over 9}} \over {{\mu _0}J\pi {a^2}}}

⇒\Rightarrow BPBQ=23{{{B_P}} \over {{B_Q}}} = {2 \over 3}

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring