State the connection between electric field and electric potential.
Two charged isolated insulating spheres X and Y are close together, as shown in Fig. 5.1. $P$ lies on the line joining the centres of the spheres. Explain why the total electric potential and the resultant electric field cannot both be zero at point $P$ at the same time.
The magnitudes of the charges on spheres X and Y in Fig. 5.1 are $Q$ and $2Q$ respectively. Treat the spheres as point charges at their centres. Point $P$ is a distance $x$ from the centre of sphere X. The electric potential at point $P$ is zero. Show that the distance $y$ of point $P$ from the centre of sphere Y is equal to $2x$.
State an expression, in terms of $Q$, $x$ and the permittivity of free space $\epsilon_0$, for the electric field strength $E_X$ at $P$ due to sphere X.
Determine an expression, in terms of $Q$, $x$ and $\epsilon_0$, for the resultant electric field strength $E$ at point $P$ due to the two spheres.
State an expression, in terms of $Q$, $x$ and the permittivity of free space $\varepsilon_0$, for the electric field strength $E_X$ at $P$ due to sphere X.
Determine an expression, in terms of $Q$, $x$ and $\varepsilon_0$, for the resultant electric field strength $E$ at point $P$ due to the two spheres.