A hollow insulated conducting sphere is given a positive charge of $10\,\mu \,C$. ........$\mu \,C{m^{ - 2}}$ will be the electric field at the centre of the sphere if its radius is $2$ meters

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

The electric field due to a uniformly charged sphere of radius $R$ as a function of the distance $r$ from its centre is represented graphically 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

If an insulated non-conducting sphere of radius $R$ has charge density $\rho $. The electric field at a distance $r$ from the centre of sphere $(r < R)$ will be

An infinitely long solid cylinder of radius $R$ has a uniform volume charge density $\rho $. It has a spherical cavity of radius $R/2$ with its centre on the axis of the cylinder, as shown in the figure. The magnitude of the electric field at the point $P$, which is at a distance $2R$ from the axis of the cylinder, is given by the expression $\frac{{23\rho R}}{{16K{\varepsilon _0}}}$ .The value of $K$ is