Conduction electrons are almost uniformly distributed within a conducting plate. When placed in an electrostatic field $\overrightarrow E $, the electric field within the plate

Aspherical shell with an inner radius $'a'$ and an outer radius $'b' $ is made of conducting material. Apoint charge $+Q$ is placed at the centre of the spherical shell and a total charge $- q $ is placed on the shell.

Assume that the electrostatic potential is zero at an infinite distance from the spherical shell. The electrostatic potential at a distance $R$ $(a < R < b)$ from the centre of the shell is (where $K = $ $\frac{1}{{4\pi {\varepsilon _0}}}$)

A solid conducting sphere of radius $a$ has a net positive charge $2Q$. A conducting spherical shell of inner radius $b$ and outer radius $c$ is concentric with the solid sphere and has a net charge $-Q$. The surface charge density on the inner and outer surfaces of the spherical shell will be

A hollow closed conductor of irregular shape is given some charge. Which of the following statements are correct ?

Consider an initially neutral hollow conducting spherical shell with inner radius $r$ and outer radius $2 r$. A point charge $+Q$ is now placed inside the shell at a distance $r / 2$ from the centre. The shell is then grounded by connecting the outer surface to the earth. $P$ is an external point at a distance $2 r$ from the point charge $+Q$ on the line passing through the centre and the point charge $+Q$ as shown in the figure. The magnitude of the force on a test charge $+q$ placed at $P$ will be