The electric field in a certain region is acting radially outward and is given by $E =Ar.$ A charge contained in a sphere of radius $'a'$ centred at the origin of the field, will be given by

A cylinder of radius $R$ and length $L$ is placed in a uniform electric field $E$ parallel to  the cylinder axis. The total flux for the surface of the cylinder is given by-

A few electric field lines for a system of two charges $Q_1$ and $Q_2$ fixed at two different points on the $\mathrm{x}$-axis are shown in the figure. These lines suggest that $Image$

$(A)$ $\left|Q_1\right|>\left|Q_2\right|$

$(B)$ $\left|Q_1\right|<\left|Q_2\right|$

$(C)$ at a finite distance to the left of $\mathrm{Q}_1$ the electric field is zero

$(D)$ at a finite distance to the right of $\mathrm{Q}_2$ the electric field is zero

An ellipsoidal cavity is carved within a perfect conductor. A positive charge $q$ is placed at the centre of the cavity. The points $A$ and $B$ are on the cavity surface as shown in the figure. Then

A metallic sphere is kept in between two oppositely charged plates. The most appropriate representation of the field lines is

Gauss’s law is true only if force due to a charge varies as