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

Three charges $q_1 = 1\,\mu c, q_2 = 2\,\mu c$ and $q_3 = -3\,\mu c$ and four surfaces $S_1, S_2 ,S_3$ and $S_4$ are shown in figure. The flux emerging through surface $S_2$ in $N-m^2/C$ is

An infinite, uniformly charged sheet with surface charge density $\sigma$ cuts through a spherical Gaussian surface of radius $R$ at a distance $x$ from its center, as shown in the figure. The electric flux $\Phi $ through the Gaussian surface is

A long cylindrical volume contains a uniformly distributed charge of density $\rho$. The radius of cylindrical volume is $R$. A charge particle $(q)$ revolves around the cylinder in a circular path. The kinetic of the particle is

Obtain Gauss’s law from the flux associated with a sphere of radius $\mathrm{'r'}$ and charge $\mathrm{'q'}$ at centre.

The electric field components in Figure are $E_{x}=\alpha x^{1 / 2}, E_{y}=E_{z}=0,$ in which $\alpha=800 \;N / C\, m ^{1 / 2} .$ Calculate

$(a)$ the flux through the cube, and

$(b)$ the charge within the cube. Assume that $a=0.1 \;m$