TS EAMCET · Physics · Electromagnetic Induction

A flat circular coil has $100$ turns of wire of radius $10 cm$ . A uniform magnetic field exists in a direction perpendicular to the plane of the coil and it grows at a rate of $0.1 T \sec^{- 1}$ , the induced emf in the coil is:

A $π V$
B $10 π V$
C $\frac{π}{10} V$
D $2 π V$

Verified Solution

Answer & Solution

Correct Answer

(C) $\frac{π}{10} V$

Step-by-step Solution

Detailed explanation

Faraday's Second Law of Electromagnetic Induction: The induced emf in a coil is equal to the rate of change of flux linkage. Therefore, Induced EMF =∆ϕ∆t=NA∆B∆t=100×π×0.12×0.1=π10 V

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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A flat circular coil has 100 turns of wire of radius 10 cm. A uniform magnetic field exists in a direction perpendicular to the plane of the coil and it grows at a rate of 0.1 T sec-1, the induced emf in the coil is:

Step-by-step Solution

A flat circular coil has $100$ turns of wire of radius $10 cm$ . A uniform magnetic field exists in a direction perpendicular to the plane of the coil and it grows at a rate of $0.1 T \sec^{- 1}$ , the induced emf in the coil is: