Concepts Of Physics MCQ Edition [Volume 2]PhysicsElectromagnetic Induction
A solenoid of 240 turns has a length of 12 cm and a radius of 2 cm . If the current in the solenoid changes at a rate of 0.8 A s ⁻¹ , determine the induced emf.
Options
- A1.2 10⁻³ V
- B6 10⁻⁵ V
- C6 10⁻⁴ V
- D3 10⁻⁴ V
Correct answer
C. 6 10⁻⁴ V
Step-by-step solution
The self-inductance of a solenoid is given by: L = ₀ N^2 A l = ₀ N^2 r^2 l Substituting the given values: L = 4 10⁻⁷ (240)^2 (0.02)^2 0.12 L = 16 ^2 10⁻¹¹ 57600 0.12 = 768 ^2 10⁻⁷ H The magnitude of the induced emf is: e = L di dt e = (768 ^2 10⁻⁷) 0.8 e = 614.4 ^2 10⁻⁷ V Using ^2 9.87 : e 614.4 9.87 10⁻⁷ 6.06 10⁻⁴ V This is approximately 6 10⁻⁴ V .