The electric field intensity at $P$ and $Q$,in the shown arrangement,are in the ratio:

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 early model for an atom considered it to have a positively charged point nucleus of charge $Ze$,surrounded by a uniform density of negative charge up to a radius $R$. The atom as a whole is neutral. For this model,what is the electric field at a distance $r$ from the nucleus?

The electric potential in a region around the origin is given by $V(x) = 4x^2$. The total charge enclosed in a cube of side $1 \ m$ centered at the origin is (in Coulombs) ...

An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet $S$ having surface charge density $+\sigma$. The electron at $t=0$ is at a distance of $1 \,m$ from $S$ and has a speed of $1 \,m/s$. The maximum value of $\sigma$ if the electron strikes $S$ at $t=1 \,s$ is $\alpha \left[ \frac{m \epsilon_0}{e} \right] \,C/m^2$. The value of $\alpha$ is:

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