Electrical Engineering ⇒ Topic : Potential at a Point Due to a Point Charge
Potential at a Point Due to a Point Charge
Consider an isolated positive charge of Q coulombs placed in a medium of relative permittivity εr. It is desired to find the electric potential at point P due to this charge. Let P be at a distance d metres from the charge. Imagine a unit positive charge (i.e. + 1 C) placed at A and situated x metres from the charge. Then the force acting on this unit charge (i.e. electric intensity) is given by [ see figure in (a)]
If this unit positive charge at A is moved through a small distance dx towards the charge +Q, then work done is given by
Total work done in bringing a unit positive charge from infinity to point P is
By definition, the work done in joules to bring a unit positive charge from infinity to point P is equal to potential at P in volts
The following points may be noted carefully
(i) The potential varies inversely with the distance d from the point charge Q. If the distance is increased three times, the potential is reduced one-third of its value and so on.
(it) Electric potential is a scalar quantity.
(iit) At d = ∞ in air/vacuum,
(iv) If Q is positive, then potential at P is *positive. On the other hand, if Q is negative, then potential at P is negative.
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