MHT CET · Physics · Magnetic Effects of Current

A solenoid of length \(0.4 \mathrm{~m}\) and having 500 turns of wire carries a current \(3 \mathrm{~A}\). A thin coil having 10 turns of wire and radius \(0.1 \mathrm{~m}\) carries current \(0.4 \mathrm{~A}\). the torque required to hold the coil in the middle of the solenoid with its axis perpendicular to the axis of the solenoid is \(\left(\mu_0=4 \pi \times 10^{-7}\right.\) SI units, \(\left.\pi^2=10\right)\left(\sin 90^{\circ}=1\right)\)

A \(3 \times 10^{-4} \mathrm{Nm}\)
B \(12 \times 10^{-4} \mathrm{Nm}\)
C \(6 \times 10^{-4} \mathrm{Nm}\)
D \(24 \times 10^{-4} \mathrm{Nm}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(6 \times 10^{-4} \mathrm{Nm}\)

Step-by-step Solution

Detailed explanation

The equation for torque is given by:
\(
\tau=\text { NIAB } \sin \theta
\)
As axis of coil and solenoid are perpendicular to each other, \(\theta=90^{\circ}\) and \(\sin \theta=1\)
\(\therefore \tau =\mu_0 \mathrm{nI}_1 \times \mathrm{NIA}\)
\(=4 \pi \times 10^{-7} \times \frac{500}{0.4} \times 3 \times 10 \times 0.4 \times \pi \times 10^{-2}\)
\(\tau =6 \times 10^{-4} \mathrm{Nm}\)
[Note: The answer of the question is not mentioned as an option.]

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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