 Solution

ID: past-exam-of-the-physics-2-paper-of-the-university-of-oxford/2014/8/2/solution

Put charges

+ Q

and

- Q

on the concentric conductors. Gauss's law gives

E (r) = Q / (4 π ϵ_{0} r^{2})

between them,

a < r < 2 a

. The potential difference is

Δ V = \int_{a}^{2 a} \frac{Q}{4 π ϵ _{0} r ^{2}} d r = \frac{Q}{8 π ϵ _{0} a} .

C = \frac{Q}{Δ V} = 8 π ϵ_{0} a .

The conductors are equipotentials; a uniform dielectric filling would replace

ϵ_{0}

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