Electric field at a point varies as ${r^o}$ for

Two fixed, identical conducting plates $(\alpha $ and $\beta )$, each of surface area $S$ are charged to $-\mathrm{Q}$ and $\mathrm{q}$, respectively, where $Q{\rm{ }}\, > \,{\rm{ }}q{\rm{ }}\, > \,{\rm{ }}0.$ A third identical plate $(\gamma )$, free to move is located on the other side of the plate with charge $q$ at a distance $d$ as per figure. The third plate is released and collides with the plate $\beta $. Assume the collision is elastic and the time of collision is sufficient to redistribute charge amongst $\beta $ and $\gamma $.

$(a)$ Find the electric field acting on the plate $\gamma $ before collision.

$(b)$ Find the charges on $\beta $ and $\gamma $ after the collision.

$(c)$ Find the velocity of the plate $\gamma $ after the collision and at a distance $d$ from the plate $\beta $.

Graphical variation of electric field due to a uniformly charged insulating solid sphere of radius $R$, with distance $r$ from the centre $O$ is represented by:

A solid metallic sphere has a charge $ + \,3Q$. Concentric with this sphere is a conducting spherical shell having charge $ - Q$. The radius of the sphere is $a$ and that of the spherical shell is $b(b > a)$. What is the electric field at a distance $R(a < R < b)$ from the centre

A conducting sphere of radius $10\, cm$ has unknown charge. If the electric field at a distance $20\, cm$ from the centre of the sphere is $1.2 \times 10^3\, N\, C^{-1}$ and points radially inwards. The net charge on the sphere is

At a point $20\, cm$ from the centre of a uniformly charged dielectric sphere of radius $10\, cm$, the electric field is $100\, V/m$. The electric field at $3\, cm$ from the centre of the sphere will be.......$V/m$