TS EAMCET · Physics · Magnetic Effects of Current

A circular coil of 10 turns and radius \(10 \mathrm{~cm}\) is placed in a uniform magnetic field of \(0.1 \mathrm{~T}\) normal to the plane of the coil. If the current in the coil is \(5 \mathrm{~A}\), then the magnitude of the torque on the coil is

A \(500 \pi \mathrm{N}-\mathrm{m}\)
B \(0.05 \pi \mathrm{N}-\mathrm{m}\)
C \(0.005 \pi \mathrm{N}-\mathrm{m}\)
D Zero

Verified Solution

Answer & Solution

Correct Answer

(D) Zero

Step-by-step Solution

Detailed explanation

Magnitude of torque on the coil is given as \(\tau=|\mathbf{m} \times \mathbf{B}| \Rightarrow \tau=N I A B \sin \theta\) where, \(\theta\) is the angle between axis of loop (normal to the loop) and direction of magnetic field. Here, \(\theta=0 \quad\) So, \(\quad \tau=0\)

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.

Same subject

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From TS EAMCET

List-I (Units)	List-II (Dimensional Formulas)
A. Pa-s	(i) [L² T^-2 K^-1]
B. NmK^-1	(ii) [MLT^-3 K^-1]
C. J kg^-1 K^-1	(iii) [ML^-1T^-1]
D. Wm^-1 K^-1	(iv) [ML²T^-2K^-1]

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