Consider a long uniformly charged cylinder having constant volume charge density $\rho$ and radius $R$. $A$ Gaussian surface is in the form of a cylinder of radius $r$ such that the vertical axis of both cylinders coincide. For a point inside the cylinder $(r < R)$,the electric field is directly proportional to

As shown in the figure,a ball $B$ is suspended by a string $S$ from a large charged plate $P$ such that it makes an angle $\theta$ with the plate. The surface charge density of the plate is proportional to which of the following?

$A$ thin spherical shell of radius $R$ has charge $Q$ spread uniformly over its surface. Which of the following graphs most closely represents the electric field $E(r)$ produced by the shell in the range $0 \le r < \infty$,where $r$ is the distance from the centre of the shell?

An infinitely long thin straight wire has a uniform charge density of $\frac{1}{4} \times 10^{-2} \text{ C/m}$. What is the magnitude of the electric field at a distance of $20 \text{ cm}$ from the axis of the wire?

An infinite sheet carrying a uniform surface charge density $\sigma$ lies on the $xy$-plane. The work done to carry a charge $q$ from the point $A = a(\hat{i} + 2\hat{j} + 3\hat{k})$ to the point $B = a(\hat{i} - 2\hat{j} + 6\hat{k})$ (where $a$ is a constant with the dimension of length and $\varepsilon_{0}$ is the permittivity of free space) is

An electron revolves around an infinite cylindrical wire having a uniform linear charge density of $2 \times 10^{-8} \, C \cdot m^{-1}$ in a circular path under the influence of an attractive electrostatic field,as shown in the figure. The velocity of the electron with which it is revolving is $......... \times 10^6 \, m \cdot s^{-1}$. (Given: mass of electron $= 9 \times 10^{-31} \, kg$)