State the connection between electric field and electric potential.
Two isolated insulating spheres X and Y are positioned close together, as shown in Fig. 5.1. P is a point 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.
In Fig. 5.1, the charge magnitudes on spheres X and Y are $Q$ and $2Q$ respectively. The spheres can be treated as point charges at their centres. Point P is $x$ from the centre of sphere X. The electric potential at point P is zero.
Show that the distance $y$ from point P to the centre of sphere Y is $2x$.
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 point $P$ caused by 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 pair of spheres.