Q26. A short solenoid of radius a and n₁ number of turns per unit length and length L is kept coaxia

Q: What is the correct answer for CUET UG Physics Q26?

The correct answer is C. Mutual inductance (M) between two coaxial solenoids is determined by the magnetic flux produced by one solenoid that links with the other. Let the inner solenoid be S₁ (radius a, n₁ turns/unit length, length L) and the outer solenoid be S₂ (radius b, n₂ turns/unit length). Since S₁ is inside S₂, the magnetic field produced by the outer solenoid (S₂) will link with the inner solenoid (S₁). The magn

Q: Q26. A short solenoid of radius a and n₁ number of turns per unit length and length L is kept coaxially inside a very long solenoid of radius b and n₂ number of turns per unit length. What is the…

The correct answer is C. Mutual inductance (M) between two coaxial solenoids is determined by the magnetic flux produced by one solenoid that links with the other. Let the inner solenoid be S₁ (radius a, n₁ turns/unit length, length L) and the outer solenoid be S₂ (radius b, n₂ turns/unit length). Since S₁ is inside S₂, the magnetic field produced by the outer solenoid (S₂) will link with the inner solenoid (S₁). The magn

Q: What are the options for this CUET UG Physics question?

A. μ₀πb²n₁n₂L · B. μ₀πa²n₁n₂L² · C. μ₀πa²n₁n₂L · D. μ₀πb²n₁n₂L²

Question

Q26. A short solenoid of radius a and n₁ number of turns per unit length and length L is kept coaxially inside a very long solenoid of radius b and n₂ number of turns per unit length. What is the mutual inductance of the system.
(a) μοπb²n₁n₂L
(b) μοπα²n₁n₂L²
(c) μοπα²n₁n₂L
(d) μοπb²n₁n₂L²

FirstInTest · Accepted Answer

Mutual inductance (M) between two coaxial solenoids is determined by the magnetic flux produced by one solenoid that links with the other. Let the inner solenoid be S₁ (radius a, n₁ turns/unit length, length L) and the outer solenoid be S₂ (radius b, n₂ turns/unit length). Since S₁ is inside S₂, the magnetic field produced by the outer solenoid (S₂) will link with the inner solenoid (S₁). The magnetic field inside a long solenoid S₂ carrying current I is B₂ = μ₀n₂I. This field is uniform over the cross-sectional area of the inner solenoid. The area of the inner solenoid S₁ is A₁ = πa². The total magnetic flux (Φ₁) linked with the inner solenoid S₁ (which has N₁ = n₁L turns) due to the current in S₂ is Φ₁ = N₁ * (B₂A₁) = (n₁L) * (μ₀n₂I) * (πa²). By definition, mutual inductance M = Φ₁/I. Therefore, M = (n₁L * μ₀n₂I * πa²) / I = μ₀n₁n₂πa²L. This matches option (c).

Answer

μ₀πb²n₁n₂L

Answer

μ₀πa²n₁n₂L²

Answer

μ₀πa²n₁n₂L

Answer

μ₀πb²n₁n₂L²

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