Self inductance of a long solenoid is given by:
Correct answer: C. Option C
- A. Option A
- B. Option B
- C. Option C
- D. Option D
Explanation
The two equations that can potentially represent the self-inductance of a long solenoid are:(b) L = μ₀NI²A(c) L = μ₀n²AlHowever, it's important to note that neither of them is fully correct. Let's analyze each option:(b) L = μ₀NI²A: This equation includes the current (I) squared, which is incorrect for the self-inductance of a solenoid. Self-inductance depends on the number of turns (N) and the geometry of the solenoid (represented by its area A and length l), but not on the current flowing through it.(c) L = μ₀n²Al: This equation gets most of the terms right, but it's missing the factor of 1/2. The correct formula for the self-inductance of a long solenoid is: L = μ₀n²Al / 2Therefore, while both options (b) and (c) contain elements of the correct formula, neither is entirely accurate. The correct answer is the missing formula with the factor of 1/2 included.
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About Electromagnetic Induction
Changing magnetic flux induces an emf according to Faraday's law, while Lenz's law gives the direction that opposes the change producing it. Transformers apply induction between coils to step alternating voltage up or down, with turns ratio, current transformation and energy losses determining practical operation.
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