Let $\rho (r) = \frac{Q}{\pi R^4} r$ be the charge density distribution for a solid sphere of radius $R$ and total charge $Q$. For a point $p$ inside the sphere at distance $r_1$ from the centre of the sphere,the magnitude of the electric field is:

An electric dipole is placed on the $x$-axis in proximity to a line charge with a linear charge density of $3.0 \times 10^{-6} \, C/m$. The line charge is placed on the $z$-axis. The positive and negative charges of the dipole are at distances of $10 \, mm$ and $12 \, mm$ from the origin,respectively. If a total force of $4 \, N$ is exerted on the dipole,find the magnitude of the positive or negative charge of the dipole.

$A$ conducting sphere of radius $R = 20 \ cm$ is given a charge $Q = 16 \ \mu C$. What is the electric field $\overrightarrow{E}$ at the centre?

$A$ parallel plate capacitor consists of two metal plates. One plate is given a charge of $+q$,while the other is connected to the ground. Points $P, P_1$,and $P_2$ are taken as shown in the figure. At which point is the electric field $NOT$ zero?

At a distance $l$ from a uniformly charged long wire, a charged particle is thrown radially outward with a velocity $u$ in the direction perpendicular to the wire. When the particle reaches a distance $2l$ from the wire, its speed is found to be $\sqrt{2}u$. The magnitude of the velocity, when it is a distance $4l$ away from the wire is (ignore gravity)

An infinite line charge produces a field of $9 \times 10^4 \text{ N/C}$ at a distance of $2 \text{ cm}$. The linear charge density is . . . . . . . $\left(k = 9 \times 10^9 \text{ Nm}^2/\text{C}^2\right)$ (in $\text{ } \mu\text{C/m}$)