Question

i. State Gauss' law.
ii. In an electric dipole, at which point is the electric potential zero?

Answer 1

(i) Gauss' law : According to this law, the total flux linked with a closed surface called Gaussian surface, (the surface need not be a real physical surface, it can also be an hypothetical one) is $\left(\begin{array}{c}\frac{1}{{ϵ}_0}\end{array}\right)$ times the charge enclosed by the closed surface i.e.,
$\varphi ={\oint }_s\overrightarrow{ϵ}.\overrightarrow{dA}=\frac{1}{{ϵ}_0}\left(Q_{enc}\right)$
(ii) When a point charge is kept at equatorial line of an electric dipole, its electric potential is zero.
Potential at point P due to charge $+q,V_1=\frac{1}{4\pi {ϵ}_{0}K}\frac{q}{BP}$
Potential at point P due to charge $-q$,
$V_2=\frac{1}{4\pi {ϵ}_{0}K}\frac{q}{AP}$
Resultant electric potential at point $P,V=V_1+V_2$
$V=\frac{1}{4\pi {ϵ}_{0}K}\frac{q}{BP}-\frac{1}{4\pi {ϵ}_{0}K}\frac{q}{AP}$
$\therefore V=0$ $[\because BP=AP]$