A 30 cm long solenoid has 10 turns per cm and area of 5 cm ^2 . The current through the solenoid coil varies from 2 A to 4 A in 3.14 s. The e.m.f. induced in the coil is 10⁻⁵ V. The value is ________.

Step-by-step solution

Given: Length of the solenoid, l = 30 cm = 0.3 m Number of turns per unit length, n = 10 turns/cm = 1000 turns/m Area of cross-section, A = 5 cm ^2 = 5 10⁻⁴ m ^2 Change in current, I = 4 A - 2 A = 2 A Time interval, t = 3.14 s The self-inductance of the solenoid is given by: L = ₀ n^2 A l Substituting the given values: L = 4 10⁻⁷ (1000)^2 5 10⁻⁴ 0.3 L = 4 10⁻⁷ 10^6 1.5 10⁻⁴ L = 6 10⁻⁵ H The magnitude of the induced e.m.f. is: e = L I t Substituting the values of L , I , and t : e = 6 10⁻⁵ 2 3.14 Using 3.14 : e = 6