A uniform charge of 3.14 10⁻⁶ C is distributed over a circular ring having a radius of 20.0 cm . The ring is rotating about its axis with an angular velocity of 60.0 rad s ⁻¹ . Determine the ratio of the electric field to the magnetic field at a point located on the axis at a distance of 5.00 cm from the centre.

Step-by-step solution

The electric field E at a distance x on the axis of a uniformly charged ring is given by: E = 1 4 ₀ q x (R^2 + x^2)^ 3/2 The magnetic field B at a distance x on the axis of a circular current loop is: B = ₀ i R^2 2 (R^2 + x^2)^ 3/2 The equivalent current i due to the rotating charge is: i = q T = q 2 Substituting i into the expression for B : B = ₀ q R^2 4 (R^2 + x^2)^ 3/2 Taking the ratio of E to B : E B = 1 4 ₀ q x (R^2 + x^2)^ 3/2 ₀ q R^2 4 (R^2 + x^2)^ 3/2 = x ₀ ₀ R^2 Using the relation c = 1 ₀ ₀ , we get: E B