Four point charges -Q, -q, 2q and 2Q are placed, one at each corner of the square. The relation between Q and

Question

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

Accepted Answer

1. **Formula for Potential:** The electric potential $V$ at a distance $r$ from a point charge $q$ is given by $V = \frac{1}{4\pi\varepsilon_0} \frac{q}{r}$ [1].
2. **Superposition Principle:** The total potential at a point due to a system of charges is the algebraic sum of the potentials due to the individual charges [2].
3. **Application to Square:** Let the distance from the centre of the square to each corner be $r$. Since the point is the centre, $r$ is the same for all four charges.
4. **Calculation:** The total potential $V_{center}$ is:
   $V_{center} = \frac{1}{4\pi\varepsilon_0 r} (-Q - q + 2q + 2Q)$
   For the potential to be zero ($V_{center} = 0$), the term in the parentheses must be zero:
   $-Q - q + 2q + 2Q = 0$
   $Q + q = 0$
   $Q = -q$

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