A long solenoid of diameter 0.1 m has 2 x 104 turns per metre. At the...
Concepts Used:
- Faraday's Law of Electromagnetic Induction
- Mutual Inductance
Explanation:
Step 1: Calculate the change in magnetic flux through the coil
- Initial current in the solenoid, I1 = 2 A
- Final current in the solenoid, I2 = -2 A
- Time taken for the current change, Δt = 0.08 s
- Rate of change of current, dI/dt = (I2 - I1) / Δt = (-2 - 2) / 0.08 = -50 A/s
- Magnetic field inside the solenoid, B = μ0 * n * I, where n is the number of turns per unit length
- Initial magnetic flux through the coil, Φ1 = π * (0.01)^2 * μ0 * 2 * 10^4
- Final magnetic flux through the coil, Φ2 = π * (0.01)^2 * μ0 * 2 * 10^4
- Change in magnetic flux, ΔΦ = Φ2 - Φ1
Step 2: Calculate the induced emf in the coil
- According to Faraday's Law of Electromagnetic Induction, the induced emf in the coil is given by:
emf = -N * dΦ/dt
- Here, N is the number of turns in the coil
- Since the coil is placed inside the solenoid, the magnetic flux change through the coil is due to the changing magnetic field of the solenoid
- Therefore, dΦ/dt = -M * dI/dt, where M is the mutual inductance between the solenoid and the coil
- Substituting the values, we get:
emf = N * M * 50
Step 3: Calculate the mutual inductance
- The mutual inductance between the solenoid and the coil is given by:
M = N * Φ / I
- Substituting the values, we get:
M = 100 * π * (0.01)^2 * μ0 * 2 * 10^4 / 2
Step 4: Calculate the induced emf in the coil
- Substituting the values of N, M, and dI/dt in the emf equation, we get:
emf = 100 * π * (0.01)^2 * μ0 * 2 * 10^4 / 2 * 50 = 4π^2
Therefore, the induced emf in the coil is 4π^2 mV. Option C is correct.
A long solenoid of diameter 0.1 m has 2 x 104 turns per metre. At the...
Change in current ΔI = -2 - (+2) = -4 A.
Time taken Δt = 0.08 s. Therefore, induced emf is
So the correct choice is (C).
To make sure you are not studying endlessly, EduRev has designed NEET study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in NEET.