The current within an ideal, long solenoid is varied at a constant rate of 0.01 A s ⁻¹ . The solenoid comprises 2000 turns/m and possesses a radius of 6.0 cm . Consider a circle of radius 1.0 cm placed inside the solenoid such that its axis aligns with the axis of the solenoid. Determine the electric field induced at a point on the circumference of this circle.

Step-by-step solution

The magnetic field inside an ideal long solenoid is given by: B = ₀ n i The rate of change of the magnetic field is: dB dt = ₀ n di dt According to Faraday's law of induction, the induced electromotive force along a circular path of radius r inside the solenoid is: E d l = | d dt | Since the electric field E is uniform along the circumference due to symmetry, and the magnetic flux is = B r^2 (as the circle is completely inside the solenoid, r E (2 r) = r^2 dB dt E = r 2 dB dt = 1 2 r ₀ n di dt Substituting the give