Final answer:
To calculate the time required to reduce the magnetic field inside a solenoid to zero, we apply Faraday's Law of electromagnetic induction and use the solenoid's initial magnetic field, the number of turns, and diameter, along with the average induced emf.
Step-by-step explanation:
The problem involves calculating the time period required to decrease the magnetic field inside a solenoid to zero, given the initial magnetic field, number of turns, diameter of the solenoid, and the average induced emf. We use Faraday's Law of electromagnetic induction, which states that the induced emf in a coil is equal to the negative rate of change of magnetic flux through the coil.
We first calculate the cross-sectional area A of the solenoid using the diameter d with the formula A = π (d/2)^2. Then, we calculate the magnetic flux Φ = B ⋅ A, where B is the magnetic field. The induced emf ε is related to the rate of change of flux (dΦ/dt) by ε = - N ⋅ (dΦ/dt), where N is the number of turns in the solenoid. By substituting the values and rearranging, we find the time Δt it takes for the field to reduce to zero.
Solving, we find the cross-sectional area A, magnetic flux Φ, and finally use ΔΦ/Δt = B ⋅ A/Δt to find the time Δt by Δt = -N ⋅ B ⋅ A / ε. Plugging in the values for N, B, A, and ε gives us the required time period.