KCET · Physics · Magnetic Effects of Current
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
- A \(1.5 \times 10^{-6} \mathrm{~N}-\mathrm{m}\)
- B \(1.5 \times 10^{-8} \mathrm{~N}-\mathrm{m}\)
- C \(1.5 \times 10^{+6} \mathrm{~N}-\mathrm{m}\)
- D \(1.5 \times 10^{+8} \mathrm{~N}-\mathrm{m}\)
Answer & Solution
Correct Answer
(B) \(1.5 \times 10^{-8} \mathrm{~N}-\mathrm{m}\)
Step-by-step Solution
Detailed explanation
We have, \(M=N I A\)
\(B=\mu_{0} n I\)
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, \(C=M B\)
\(B=\mu_{0} n I\)
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, \(C=M B\)
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