Concepts Of Physics MCQ Edition [Volume 2]PhysicsElectromagnetic Induction
The current flowing through an ideal, long solenoid varies at a uniform rate of 0.01 A s ⁻¹ . The solenoid has 2000 turns/m and a radius of 6.0 cm . Determine the electric field induced at a point situated outside the solenoid, at a perpendicular distance of 8.0 cm from its axis.
Options
- A2.83 10⁻⁷ V m ⁻¹
- B5.65 10⁻⁷ V m ⁻¹
- C1.13 10⁻⁶ V m ⁻¹
- D1.01 10⁻⁶ V m ⁻¹
Correct answer
B. 5.65 10⁻⁷ V m ⁻¹
Step-by-step solution
The magnetic field inside an ideal long solenoid is given by B = ₀ n i . The magnetic flux through a circular loop of radius r ( r > R ) coaxial with the solenoid is confined to the area of the solenoid: = B R^2 = ₀ n i R^2 By Faraday's law of induction, the magnitude of the induced electromotive force is: = d dt = ₀ n R^2 di dt The induced electric field E along the circular loop of radius r is related to the induced emf by: = E d l = E(2 r) Equating the two expressions for : E(2 r) = ₀ n R^2 di dt E = ₀ n R^2 2r