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JIPMER 2015
Exam
JIPMER
Year
2015
Subject
Physics
Chapter
Magnetic Effects of Current

JIPMER 2015 · Physics · Magnetic Effects of Current

The parts of two concentric circular arcs joined by two radial...

The parts of two concentric circular arcs joined by two radial lines and carries current ii. The arcs subtend an angle θ\theta at the centre of the circle. The magnetic field at the centre OO, is

Options

  1. Aμ0i(b−a)θ4πab\frac{\mu_0 i(b-a) \theta}{4 \pi a b}
  2. Bμ0i(b−a)(π−θ)\frac{\mu_0 i(b-a)}{(\pi-\theta)}
  3. Cμ0i(b−a)θπab\frac{\mu_0 i(b-a) \theta}{\pi a b}
  4. Dμ0i(a−b)2πab\frac{\mu_0 i(a-b)}{2 \pi a b}

Correct answer

A. μ0i(b−a)θ4πab\frac{\mu_0 i(b-a) \theta}{4 \pi a b}

Step-by-step solution

The field at the centre of a circular loop is given by B=μ0i2aB=\frac{\mu_0 i}{2 a} The field due to circular arc of inner circle is B1=(θ2π)μ0i2aB_1=\left(\frac{\theta}{2 \pi}\right) \frac{\mu_0 i}{2 a} The field due to circular arc of outer circle is B2=(θ2π)(μ0i2b)B=B1−B2=μ0i(b−a)θ4πab\begin{aligned} B_2 & =\left(\frac{\theta}{2 \pi}\right)\left(\frac{\mu_0 i}{2 b}\right) \\ B & =B_1-B_2=\frac{\mu_0 i(b-a) \theta}{4 \pi a b}\end{aligned}
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