Question

An infinite line charge is at the axis of a cylinder of length 1 m and radius 7 cm . If electric field at any point on the curved surface of cylinder is 250 $N{C}^{-1},$ then net electric flux through the cylinder is:

Answer 1

An infinite line charge passes through axis of a cylinder-

Electric field at point $P$ is $E=250N/C$

Due to symmetry electric field is same for all points along the curved surface of the cylinder. [line charge shows cylindrical symmetry]

Now, flux through top and bottom circular surface is zero, as their Area vectors $\left(\overrightarrow{A}\right)$ is perpendicular to field $\overrightarrow{E}$, So, $\theta =\overrightarrow{E}.\overrightarrow{A}=o$

So, all flux passes through curved surface, given by-

$\theta =EA$, where $A=2\pi rL$, curved surface area

$=E.2\pi RL$

$\theta =250\times 2\times \pi \times 0.07\times 1=109.96N{m}^2/c$