Given:

Charge of the ring(q) = 3.14 × 10^–6 C

Radius of circular ring(r) = 20 cm = 0.2 m

Angular velocity with which the ring rotates(w) = 60 rad s^-1

Diagram:

E₁ and E₂ denote the electric field due to two point elements 1 and 2 on the circumference of the circular loop. The resultant electric field due to them is E. Similarly, the resultant magnetic field due to the them is B.

Formula used:

Electric field due to a circular loop(E),

where q = charge carried by the ring, x = distance from the center, r = radius of the ring, ϵ₀ = electric permittivity of vacuum = 8.85 X 10^-12 N m² C^-2

Magnetic field due to a current carrying loop(B),

where μ₀ = magnetic permeability of vacuum = 4π x 10^-7 T m A^-1, i = current carried by the loop, r = radius of the loop, x = distance from the center

Now, i = q/t, where i = current, q = charge, t = time taken.

Angular velocity(w) = 60 rad/s (given)

Hence, time period of one revolution(T) = 2π/w = 2π/60 s

Hence, current(i) = charge per unit time = q/T = 60q/2π = 30q/π A, where q = charge, T = time period of revolution

Therefore, E/B = (2 x 3.14 × 10^–6 x 0.05 x 9 x 10⁹ x 3.14)/ (4 x 3.14 x 10^-7 x 30 x 3.14 × 10^-6 x 0.2²) = 1.88 x 10¹⁵ ms^-1 (Ans)