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 square is zero 1.Q=-q , 2.Q=-1/q , 3.Q=q 4.Q=1/q​

Answer 1

Electric potential:

• $\rm V = \dfrac{KQ}{r}$
• It is a scalar quantity.
• Q = charge creating the field , r = distance where potential to be find.

Solution:

According to the image attached,

Net potential will be the result of potential of each charge at the center.

$\implies\rm V_{net} = V_A +V_B +V_C +V_D$

$\implies\rm V_{net} = \dfrac{K(-Q)}{r} + \dfrac{K(-q)}{r}+\dfrac{K2q}{r}+\dfrac{K2Q}{r}$

$\implies\rm 0 = - \dfrac{KQ}{r} - \dfrac{Kq}{r}+\dfrac{K2q}{r}+\dfrac{K2Q}{r}$

$\implies\rm 0 = \dfrac{K2Q}{r}- \dfrac{KQ}{r} +\dfrac{K2q}{r}-\dfrac{Kq}{r}$

$\implies\rm 0 = \dfrac{KQ}{r} +\dfrac{Kq}{r}$

$\implies\rm \dfrac{KQ}{r} = -\dfrac{Kq}{r}$

$\implies\bf Q = -q$

★The relation between q and Q for which the potential at the centre of square is zero ? --- (1) Q = -q