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  4. Two electric charge 12 μC and -6 μC are placed 20 cm apart in air. There will be a point P on the line joining these charges and outside the region between them, at which the electric potential is zero, The distance of P from -6 μC charge is

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Q. Two electric charge 12 $\mu$C and -6 $\mu$C are placed 20 cm apart in air. There will be a point P on the line joining these charges and outside the region between them, at which the electric potential is zero, The distance of P from -6 $\mu$C charge is

KEAMKEAM 2006Electrostatic Potential and Capacitance

Solution:

Let $P$ be at distance $x$ from $-6 \mu C$ charge.
We know, potential $V =\frac{ kq }{ r }$
Given, potential at $P : V _{ P }=0$
$\Rightarrow \frac{ k \times 12 \times 10^{-6}}{(0.2+ x )}+\frac{ k \times(-6) \times 10^{-6}}{ x }=0$
or, $\frac{12}{0.2+x}=\frac{6}{x}$
or, $2 x =0.2+ x$
or, $x=0.2 \,m$