Electric Potential Due To A Point Charge

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Electric Potential-

 

Electric potential at a point in an electric field is defined as-

 

It is the amount of work done by an external agent in moving a unit positive charge from infinity to that point against the electrostatic forces.

OR

It is the amount of work done by an external agent per unit charge in moving an electric charge from infinity to that point against the electrostatic forces.

 

 

Electric Potential Due To A Point Charge-

 

Consider-

  • A positive point charge Q is placed at point O.
  • We wish to calculate the electric potential at any point P located at a distance r from it.

 

 

To find the electric potential at point P, we bring a test charge q0 from infinity to point P very-very slowly and calculate the work done in this process.

 

Then, electric potential at point P would be given by-

 

 

We know, electric field is a conservative field. So, work done in a closed path is zero. So, we must have-

 

 

Thus, the above relation can be re-written as-

 

(Equation-01)

 

Now, we will calculate the work done by the external agent in taking the charge q0 from point P to infinity and then substitute in equation-01.

 

Consider the charge q0 to be present at some point O at a distance x from the charge Q during its motion from P to infinity.

 

 

NOTE

It is important to note that-

The external agent exerts an equal amount of force as exerted by the charge Q but in opposite direction so that the net force on charge q0 at any instant is zero and the charge moves towards infinity very-very slowly with a constant velocity.

 

The work done by the external agent in causing a small displacement dx is given by-

 

 

To calculate the total work done by the external agent in taking the charge from point P to infinity, we integrate the above calculated small work done as-

 

 

Substituting in equation-01, we get-

 

 

Thus, Electric potential due to a point charge Q at a distance r from it is given by-

 

(Important Formula)

 

Graph Showing The Variation of Electric Potential-

 

The following graph shows the variation of electric potential due to a point charge with distance from it-

 

 

Characteristics of Electric Potential-

 

  • Electric potential is a scalar quantity.
  • The SI unit of electric potential is volt (V).

1 V = 1 JC-1

  • Electric potential is positive due to a positive charge & negative due to a negative charge.
  • The electric potential due to a point charge is spherically symmetric.

 

Read the next article on-

Electric Potential Due To Electric Dipole

 

Get more notes & other study material of the Chapter Electrostatic Potential & Capacitance.


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