Within a spherical charge distribution of charge density $\rho \left( r \right)$, $N$ equipotential surfaces of potential ${V_0},{V_0} + \Delta V,{V_0} + 2\Delta V,$$.....{V_0} + N\Delta V\left( {\Delta V > 0} \right),$ are drawn and have increasing radii $r_0, r_1, r_2,......r_N$, respectively. If the difference in the radii of the surfaces is constant for all values of $V_0$ and $\Delta V$ then

A charge of $5\,C$ experiences a force of $5000\,N$ when it is kept in a uniform electric field. .........$V$ is the potential difference between two points separated by a distance of $1\,cm$

A cathode ray tube contains a pair of parallel metal plates $1.0\, cm$ apart and $3.0\, cm$ long. A narrow horizontal beam of electron with a velocity $3 \times 10^7\, m/s$ passed down the tube midway between the plates. When a potential difference of $550\, V$ is maintained across the plates, it is found that the electron beam is so deflected that it just strikes the end of one of the plates. Then the specific charge of the electron in $C/kg$ is

The electric potential in a region is represented as $V = 2x + 3y -z$ ; then the expression of electric field strength is

Figure shows two equipotential lines in $x, y$ plane for an electric field. The scales are marked. The $x-$ component $E_x$ and $y$ -component $E_y$ of the electric field in the space between these equipotential lines are respectively :-

The potential due to an electrostatic charge distribution is $V(r)=\frac{q e^{-\alpha e r}}{4 \pi \varepsilon_{0} r}$, where $\alpha$ is positive. The net charge within a sphere centred at the origin and of radius $1/ \alpha$ is