Two solid metal spheres A and B, each with radius $1.5\,\text{cm}$, are placed in a vacuum. The centres of the spheres are $20.0\,\text{cm}$ apart, as shown in Fig. 6.1. Both spheres have positive charge. Point P is located on the straight line joining the centres of the two spheres, at a distance $x$ from the centre of sphere A. Fig. 6.2 shows how the electric field strength $E$ at point P varies with distance $x$.
(a)[3]
Use Fig. 6.2 to determine the ratio
\[ \frac{\text{magnitude of charge on sphere A}}{\text{magnitude of charge on sphere B}}. \]
Show your working.
(b)
The electric potential $V$ at point P varies with distance $x$ as shown in Fig. 6.3.
(c(i))[3]
An $\alpha$-particle starts from rest on the surface of sphere A. The $\alpha$-particle travels along the line joining the centres of the two spheres. Determine, for the $\alpha$-particle as it moves between the two spheres, its maximum speed.
(c(ii))[2]
Determine its speed when it reaches the surface of sphere B.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “the electric field is zero at the midpoint, or $x=11\,\text{cm}$” …