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Question

Why potential energy for a test charge with negative charge on it is negative and it’s vice versa?


Solution

The electric potential Vp at  a point P due to a single point charge +Q is
Vp=Q4πϵ0r
Where r is the distance of point P from the charge +Q.
VP=9×109Qr... in free space/air
VP=9×109Qϵrr ... in a medium

If Q is positive, then potential at P is positive. On the other hand, if Q is negative, then potential at P is negative. It is reminded that electric potential is a scalar quantity.
A positive charge loses electric potential energy as it moves from high potential to low potential and vice-versa. On the other hand, a negative charge gains electric potential energy as it moves from high to low potential and vice-versa.


 

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