The electrostatic potential in a charged spherical region of radius $r$ varies as $V = ar^3 + b$, where $a$ and $b$ are constants. The total charge in the sphere of unit radius is $\alpha \times \pi a \epsilon_0$. The value of $\alpha$ is . . . . . . .

The diagram below shows electric field lines in a region of space. Which of the following diagrams best shows the variation with distance $d$ of the potential $V$ along the line $XY$ as we move from $X$ to $Y$?

The electric potential $V$ is given as a function of distance $x$ (metre) by $V = (5x^2 + 10x - 9) \text{ V}$. The value of the electric field at $x = 1 \text{ m}$ is ...... $V/m$.

The electric field at a distance $x$ from the origin is given by $E = 100/x^2$. The potential difference between the points at $x = 10 \, m$ and $x = 20 \, m$ is ...... $V$.

An electric field $\vec{E} = (25 \hat{i} + 30 \hat{j}) \, NC^{-1}$ exists in a region of space. If the potential at the origin is taken to be zero,then the potential at $x = 2 \, m, y = 2 \, m$ is ...... $volt$.

An infinite non-conducting sheet has a surface charge density of $7 \times 10^{-7} \text{ C m}^{-2}$ on one side. The distance between equipotential surfaces whose potentials differ by $19.8 \text{ V}$ will be (Take $\frac{1}{4 \pi \varepsilon_{0}} = 9 \times 10^9 \text{ SI units}$) (in $\text{ mm}$)