A positively charged isolated metal sphere has radius $R$, as in Fig. 5.1. The line XY passes through the sphere’s centre. Point P is on line XY and is a variable displacement $x$ from the centre of the sphere. Point Q is fixed and is not on line XY. The electric field strength at the surface of the sphere is $E_0$.
(a)[3]
Explain why the electric potential close to an isolated proton is positive.
(b(i))[1]
On Fig. 5.1, draw an arrow at point Q to indicate the direction of the electric field there.
(b(ii))[3]
On Fig. 5.2, sketch the way the electric field $E$ at point P varies with $x$ for values of $x$ from $x=-3R$ to $x=3R$. Do not show the region inside the sphere between $x=-R$ and $x=R$.
(c)[2]
The proton and the electron in a hydrogen atom are separated by a distance of $5.3 \times 10^{-11}\,\text{m}$. Calculate the electric potential energy of the proton and the electron.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “potential is set to zero at infinity” …