A non-conducting solid disc of mass m = 2 kg and total charge q = +1 C is placed vertically on a rough horizontal non-conducting surface. The coefficient of static friction is μ = 0.2. A uniform horizontal electric field E is switched on. Find the maximum value of E, in N C⁻¹, for which the disc rolls without slipping. Take g = 10 m s⁻².

Question

G1 Physics · Accepted Answer

The electric force qE acts through the centre. Let friction be f. Translation: qE - f = ma. Rotation: fR = Iα. For a solid disc, I = (1/2)mR² and pure rolling gives α = a/R, so f = ma/2. Hence qE = 3ma/2 and f = qE/3. The limiting condition is f = μmg = 4 N. Thus qE/3 = 4. With q = 1 C, E = 12 N C⁻¹.