Q103 / 180 · AIIMS 2019 (25 May) · Physics

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. Figure

  • Correct answer
    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

The magnetic force on a conductor, $F=B i \ell$ Magnetic force per unit length, $\frac{F}{\ell}=B i=\left(\frac{\mu_0 i^2}{4 r}\right)$

Hence, the correct answer is option: 'A'.

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