The inductance of a solenoid can be calculated using the formula:
L = (μ₀ * n² * A * l) / (l + 0.5 * d)
where:
L is the inductance in henries (H)
μ₀ is the permeability of free space (4π × 10^-7 T·m/A)
n is the number of turns
A is the cross-sectional area of the solenoid
l is the length of the solenoid
d is the diameter of the solenoid (assumed to be negligible for a long, thin solenoid)
Substituting the given values, we get:
L = (4π × 10^-7 T·m/A * 435² * 3.10 × 10^-9 m² * 0.055 m) / (0.055 m + 0.5 * 0)
L = 7.85 × 10^-4 H
Therefore, the inductance of the solenoid is 7.85 × 10^-4 H.
Note: The unit for inductance is henries (H), named after the American scientist Joseph Henry.
(b) the average emf (in V)
The average emf induced in the solenoid can be calculated using Faraday's Law of Electromagnetic Induction, which states that the emf induced in a conductor is proportional to the rate of change of magnetic flux through the conductor. The formula for the emf induced in a solenoid is:
emf = -L * ΔI / Δt
where:
emf is the induced emf in volts (V)
L is the inductance in henries (H)
ΔI is the change in current in amperes (A)
Δt is the time interval over which the current changes in seconds (s)
Substituting the given values, we get:
emf = -(7.85 × 10^-4 H) * (-6.00 A) / (7.83 × 10^-3 s)
emf = 5.99 V
Therefore, the average emf induced in the solenoid is 5.99 V.