Electrostatics

Under the influence of the Coulomb field of charge $+Q$, a charge $-q$ is moving around it in an elliptical orbit. Find out the correct statement(s).

A solid sphere of radius $R$ has a charge $Q$ distributed in its volume with a charge density $\rho=\kappa r^a$, where $\kappa$ and $a$ are constants and $r$ is the distance from its centre. If the electric field at $r=\dfrac R2$ is $\dfrac18$ times that at $r=R$, find the value of $a$.

Consider a system of three charges $\frac q3$, $\frac q3$ and $-\frac{2q}3$ placed at points A, B and C, respectively, as shown in the figure. Take O to be the centre of the circle of radius $R$ and angle CAB = 60°.

STATEMENT-1: For practical purposes, the earth is used as a reference at zero potential in electrical circuits.

and

STATEMENT-2: The electrical potential of a sphere of radius $R$ with charge $Q$ uniformly distributed on the surface is given by $\dfrac{Q}{4\pi\varepsilon_0R}$.

The electric field at $r=R$ is

For $a=0$, the value of $d$ (maximum value of $\rho$ as shown in the figure) is

The electric field within the nucleus is generally observed to be linearly dependent on $r$. This implies

A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral.

Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then,

A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is

Positive and negative point charges of equal magnitude are kept at $\left(0,0,\frac a2\right)$ and $\left(0,0,\frac{-a}2\right)$, respectively. The work done by the electric field when another positive point charge is moved from $(-a,0,0)$ to $(0,a,0)$ is