Two electric charges $12\,\mu C$ 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 the $-6\,\mu C$ charge is.......$m$.

Which of the following statements is correct?

Two particles $A$ and $B$ having the same mass have charges $+q$ and $+4q$ respectively. When they are allowed to fall from rest through the same electric potential difference,the ratio of their speeds $v_A$ to $v_B$ will be:

An arc of radius $r$ carries a charge. The linear charge density is $\lambda$ and the arc subtends an angle of $\frac{\pi}{3}$ at the centre. What is the electric potential at the centre?

There is a uniform electrostatic field in a region. The potential at various points on a small sphere centered at $P$,in the region,is found to vary between the limits $589.0\,V$ to $589.8\,V$. What is the potential at a point on the sphere whose radius vector makes an angle of $60^o$ with the direction of the field (in $,V$)?

$A$ uniform electric field exists in the positive $x$-direction. Let $A$ be the origin. Point $B$ is at $x = +1 \ cm$ on the $x$-axis and point $C$ is at $y = +1 \ cm$ on the $y$-axis. Which of the following relations is correct regarding the potentials at $A, B,$ and $C$?