Past exam of the physics 2 paper of the University of Oxford / 2016 / 9 / c

Inserting an independently biased conducting sphere makes two vacuum gaps, each with its own constant radial electric flux. Let $A_1$ and $A_2$ be the coefficients of $1/r^2$. The two potential drops areThereforeThe middle conductor can carry net electric charge, so $A_1$ and $A_2$ need not be equal. Its charge is $4\pi {ϵ}_0(A_2-A_1)$, consistent with the jump in the normal electric field. For $0<V_2<V_1$ both fields point outwards; outside that interval one of the gap fields reverses direction.