Conduction electrons are almost uniformly distributed within a conducting plate. When placed in an electrostatic field $\overrightarrow E $, the electric field within the plate
Is zero
Depends upon $E$
Depends upon $\overrightarrow E $
Depends upon the atomic number of the conducting element
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
The electric field near a conducting surface having a uniform surface charge density $\sigma $ is given by
$(a)$ A conductor $A$ with a cavity as shown in Figure $(a)$ is given a charge $Q$. Show that the entire charge must appear on the outer surface of the conductor.
$(b)$ Another conductor $B$ with charge $q$ is inserted into the cavity keeping $B$ insulated from $A$. Show that the total charge on the outside surface of $A \text { is } Q+q$ [Figure $(b)$]
$(c)\;A$ sensitive instrument is to be shielded from the strong electrostatic fields in its environment. Suggest a possible way.
An empty thick conducting shell of inner radius $a$ and outer radius $b$ is shown in figure.If it is observed that the inner face of the shell carries a uniform charge density $-\sigma$ and the surface carries a uniform charge density $ '\sigma '$
If a point charge $q_A$ is placed at the center of the shell, then choose the correct statement $(s)$
A metallic spherical shell has an inner radius ${{\rm{R}}_1}$ and outer radius ${{\rm{R}}_2}$. A charge $\mathrm{Q}$ is placed at the centre of the spherical cavity. What will be surface charge density on $(i)$ the inner surface, and $(ii)$ the outer surface ?