Potential Due to a Point Charge
The battery is used in many devices like a torch, laptop, clock, bike, etc.
The battery is used in the motorcycle to illuminate light in the night.
Suppose, a motorcycle battery and a car battery have the same voltage.
It means the same potential difference between the terminals of the battery.
But, the car battery store much more energy than the motorcycle battery.
Because, the amount of charges moves in the car's battery is faster than the motorcycle's battery.
The work needed to move this charge from a reference point to a specific point is called the electric potential.
Now, we will derive the expression of electric potential due to a point charge.
Let's derive an expression of electric potential due to point charge.
Suppose, we consider a positive point charge
placed at the origin
Now, we wish to calculate electric potential at point
Let us consider a point charge
be placed at point
By coulomb law, the electrostatic force
acting on charge
and permeability for free space
The work done from the charge
against the electrostatic force is,
The total work done of charge
from infinity to point
will be as,
After putting the value of
Further, solving by the integration of the equation from
Hence, we get the work done
as mentioned above.
Now, as the electric potential at point
So, after putting the value of
in the above equation, we get the potential due to point charge.
So, we have understood the electric potential due to point charge.
By coulomb law, the electrostatic force,
And as the electric potential is as,
Hence, after putting the values, we get the value of the electric potential at point charge.