Physics 9702 · AS & A Level · Capacitors and capacitance

Capacitors and capacitance — practice question

An isolated conducting sphere in a vacuum has a capacitance of $69\,\text{pF}$, and the sphere carries a charge of $+83\,\text{pC}$.
(a)[1]

Define the electric field at a point.

(b(i))[2]

On Fig. 6.1, draw field lines to show the electric field outside the sphere caused by the charge on the sphere.

(b(ii))[2]

Calculate the electric potential at the surface of the sphere.

(b(iii))[2]

Determine the sphere’s radius.

(b(iv))[2]

Calculate the electric field strength $E$ at the surface of the sphere. Include a unit in your answer.

(c)[2]

The sphere in (b) is discharged by connecting it to earth $(0\,\text{V})$ through a resistor of resistance $120\,\text{M}\Omega$. Calculate the time for the charge to decrease to $26\,\text{pC}$.

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