An air-cored solenoid with length 30 ~cm , area of cross-section 25 ~cm ^2 and number of turns 500 carries a current of 2.5 ~A . The current is suddenly switched off for a brief time of 10⁻³ ~s . How much is the (nearly) average back e.m.f. induced across the ends of the open switch in the circuit? (Ignore the variation of magnetic field near the ends of solenoid)

Step-by-step solution

Field at the centre of the solenoid with N turns over length l is : B= ₀ ( N l ) i The self-flux associated with the coil with area A is: =N(B A) We define self-inductance L as, =L i Therefore, self-inductance of the solenoid is given by, L= i = N(B A) i = N [ ₀ ( N l ) i A ] i = ₀ N^2 A l Back emf, aligned & e=L ( d i d t )= ( ₀ N^2 A l ) d i d t = 4 10⁻⁷ 500 500 25 10⁻⁴ 0.3 2.5 10⁻³ ~V & e=6.5 ~V aligned