AP EAMCET · PHYSICS · Electromagnetic Induction

A solenoid of length $60 cm$ with $15$ turns per $cm$ and area of cross section $4 \times 10^{- 3} m^{2}$ completely surrounds another co-axial solenoid of same length and area of cross-section $2 \times 10^{- 3} m^{2}$ with $40$ turns per $cm$ . Mutual inductance of the system is

A $9 mH$
B $6 mH$
C $3 mH$
D $10 mH$

Verified Solution

Answer & Solution

Correct Answer

(A) $9 mH$

Step-by-step Solution

Detailed explanation

Given, Area of the inner solenoid, A=2×10-3 Mutual inductance of the system, M=μ0n1n2AI ⇒M=4π×10-7×1000×4000×2×10-3×60×10-3 ⇒M=9 mH

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

Explore more questions on app

From AP EAMCET

Explore more questions on app

A solenoid of length 60 cm with 15 turns per cm and area of cross section 4×10-3 m2 completely surrounds another co-axial solenoid of same length and area of cross-section 2×10-3 m2 with 40 turns per cm. Mutual inductance of the system is

Step-by-step Solution

A solenoid of length $60 cm$ with $15$ turns per $cm$ and area of cross section $4 \times 10^{- 3} m^{2}$ completely surrounds another co-axial solenoid of same length and area of cross-section $2 \times 10^{- 3} m^{2}$ with $40$ turns per $cm$ . Mutual inductance of the system is