Question 67: Electrostats & Capacitance

Question

Point charges $-3 Q,-q, 2 q$ and $2 Q$ are placed, one at each corner of a square. The relation between Q and q for which the potential at the centre of the square is zero is

Accepted Answer

Let the side of the square be $a$. Every corner is at the same distance $r=	frac{a}{\sqrt2}$ from the centre, so the total potential there is proportional to the sum of the charges.
Write the potentials (up to the common factor $k/r$):
$      V_{m tot}\propto(-3Q)+(-q)+(2q)+(2Q).    $
Sum them:
$      (-3Q+2Q)\;+\;(-q+2q)\;=\;-Q+q.    $
Set $V_{m tot}=0$ Ã¢ÂÂ $-Q+q=0$ Ã¢ÂÂ
$      q=Q.    $
So the required relation is
$    \boxed{Q=q}, $
which is Option D.

Answer

$Q=\frac{1}{q}$

Answer

$Q=-q$

Answer

$Q=\frac{-1}{q}$

Answer

$Q=q$

Electrostats & Capacitance

Point charges -3 Q,-q, 2 q and 2 Q are placed, one at each corner of a square. The relation between Q and q for which the potential at the centre of the square is zero is

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