Question

Two non-conducting plates $A$ and $B$ of radii $2R$ and $4R$ respectively are kept at distances $x$ and $2x$ from the point charge $q$. A surface cutout of a non conducting shell $C$ is kept such that its centre coincides with the point charge. Each plate and the spherical surface carries a surface charge density $\sigma$. If $F_A,F_B$ and $F_C$ be the forces on plate $A$ plate $B$ and spherical surface $C$ due to charge $q$ respectively. Find a relation between $F_A,F_B$ and $F_C$ .

Answer 1

From Gauss law,

$E\cdot dA=\frac{q}{{\epsilon }_o}$

And hence, using that electric field due to each circular plate is given by,

$E=\frac{\sigma }{2{\epsilon }_o}$

$\therefore$ Hence, force between spherical surface and charge is given by,

$F^{\gamma }=q{E}^{\gamma }=\frac{q\sigma }{2{\epsilon }_o}$

$\therefore F_A^{\gamma }=F_B^{\gamma }=F_C^{\gamma }=\frac{\sigma q}{2{\epsilon }_o}$