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Question: Answered & Verified by Expert
A semicircular arc of radius $r$ and a straight wire along the diameter, both are carrying same current $i$. Find out magnetic force per unit length on the small element $P$, which is at the centre of curvature.

PhysicsMagnetic Effects of CurrentAIIMSAIIMS 2019 (25 May)
Options:
  • A $\left(\frac{\mu_0 i^2}{4 r}\right)$
  • B $\left(\frac{\mu_0 i^2}{2 r}\right)$
  • C $\left(\frac{\mu_0 i^2}{r}\right)$
  • D $\left(\frac{2 \mu_0 i^2}{r}\right)$
Solution:
1325 Upvotes Verified Answer
The correct answer is: $\left(\frac{\mu_0 i^2}{4 r}\right)$
The magnetic force on a conductor, $F=B i \ell$
Magnetic force per unit length,
$\frac{F}{\ell}=B i=\left(\frac{\mu_0 i^2}{4 r}\right)$

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