Q159 / 180 · KCET 2011 · Physics

The torque required to hold a small circular coil of 10 turns, area $1 \mathrm{~mm}^{2}$ and carrying a current of $\left(\frac{21}{44}\right)$ A in the middle of a long solenoid of $10^{3}$ turns/m carrying a current of $2.5 \mathrm{~A}$, with its axis perpendicular to the axis of the solenoid is
Figure

  • A
    $1.5 \times 10^{-6} \mathrm{~N}-\mathrm{m}$
  • Correct answer
    B
    $1.5 \times 10^{-8} \mathrm{~N}-\mathrm{m}$
  • C
    $1.5 \times 10^{+6} \mathrm{~N}-\mathrm{m}$
  • D
    $1.5 \times 10^{+8} \mathrm{~N}-\mathrm{m}$

Solution

We have, $M=N I A$ $\quad B=\mu_{0} n I$ Here, $C=\left(n_{1} I_{1} A\right)\left(\mu_{0} n_{2} I_{2}\right)$ $=\left(10 \times \frac{21}{44} \times 10^{-6}\right)\left(4 \times \frac{22}{7} \times 10^{-7} \times 10^{3} \times 2.5\right)$ $=1.5 \times 10^{-8}$ N-m $\quad$ Torque, $C=M B$

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

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