Question

A uniform electric field $E=500N/C$ passes through a hemispherical surface of radius $R=1.2m$ as shown in the figure. The net electric flux (in SI units) through the hemispherical surface only in $N\pi$. Find the value of N.

Answer 1

To calculate flux, we always take the projectional surface area.
$\therefore$ Projectional area of hemispherical surface of radius R would be a circle of area $\pi R^2$
Also, the angle between electric field and area vector of circle is ${37}^0[{90}^0-{53}^0={37}^0]$
$\varphi =E.S=EScos{37}^0=E.\pi R^{2}cos{37}^0$



Given, $E=500N{C}^{-1}$,
$R=1.2m,cos{37}^0=\frac{4}{5}$
$\varphi =500\times \pi \times (1.2{)}^2\times \frac{4}{5}$
$\varphi =576\pi N{C}^{-1}{m}^2$
Also, from question:
$\varphi =N\pi N{C}^{-1}{m}^2$
$N=576$
Hence, the value of N is 576