Two point charges of magnitude $+q$ and $-q$ are placed at $\left( { - \frac{d}{2},0,0} \right)$ and $\left( {\frac{d}{2},0,0} \right)$, respectively. Find the equation of the equipotential surface where the potential is zero.
Let the required plane lies at a distance $x$ from the origin as shown in figure.
Potential at point $P,$
$\frac{k q}{\left[\left(x+\frac{d}{2}\right)^{2}+h^{2}\right]^{1 / 2}}-\frac{k q}{\left[\left(x-\frac{d}{2}\right)^{2}+h^{2}\right]^{1 / 2}}=0$
$\therefore \frac{1}{\left[\left(x+\frac{d}{2}\right)^{2}+h^{2}\right]^{1 / 2}}=\frac{1}{\left[\left(x-\frac{d}{2}\right)^{2}+h^{2}\right]^{1 / 2}}$
$\therefore\left(x-\frac{d}{2}\right)^{2}+h^{2}=\left(x+\frac{d}{2}\right)^{2}+h^{2}$
$\therefore x^{2}-x d+\frac{d^{2}}{4}=x^{2}+x d+\frac{d^{2}}{4}$
$\therefore 0=2 x d$
$\therefore x=0$
The equation of the required plane is $x=0$ means $y z$ plane.
An infinite non-conducting sheet has a surface charge density $\sigma = 0.10\, \mu C/m^2$ on one side. How far apart are equipotential surfaces whose potentials differ by $50\, V$
Two conducting hollow sphere of radius $R$ and $3R$ are found to have $Q$ charge on outer surface when both are connected with a long wire and $q'$ charge is kept at the centre of bigger sphere. Then which one is true
Electric field is always ...... to the equipotential surface at every point. (Fill in the gap)
Draw an equipotential surface of two identical positive charges for small distance.
Assertion $(A):$ A spherical equipotential surface is not possible for a point charge.
Reason $(R):$ A spherical equipotential surface is possible inside a spherical capacitor.