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 $q$ placed at the origin $O$ .

Now, we wish to calculate electric potential at point $P$ from distance $r$ from it.

Let us consider a point charge $q_{0}$ be placed at point $A$ at distance $x$ from origin $O$ .

By coulomb law, the electrostatic force $F$ acting on charge $q_{0}$ and permeability for free space $K$ is as,

The work done from the charge $q_{0}$ through displacement $d x$ against the electrostatic force is,

The total work done of charge $q_{0}$ from infinity to point $P$ will be as,

After putting the value of $F$ and $d x$ ,

Further, solving by the integration of the equation from $\infty$ to $0$ .

Hence, we get the work done $W$ as mentioned above.

Now, as the electric potential at point $P$ is,

So, after putting the value of $W$ in the above equation, we get the potential due to point charge.

So, we have understood the electric potential due to point charge.

Revision

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.

The End