Work In Moving A Charge In Electric Field

Electric Potential-

 

Before you go through this article, make sure that you have gone through the previous article on Electric Potential Due To Point Charge.

 

We have learnt-

• Electric Potential at a point is the amount of work done by external agent in moving a unit positive charge from infinity to that point.
• It is given by the formula-

 

 

In this article, we will learn about work done in moving a charge in an electric field.

 

Work Done In Moving A Charge in External Electric Field-

 

Consider-

• A positive point charge Q is fixed at a point.
• We wish to calculate the amount of work done by the external agent in moving another point charge q_o from point A to point B in the electric field of source charge Q.

 

 

Now, Consider-

• The charge q₀ is being taken by the external agent from point A to point B.
• At any instant, the charge q_o is present at some point P at a distance r from the source charge Q during its motion from A to B.

 

 

The work done by the external agent in causing a small displacement dr from point P is given by-

 

 

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

 

 

From here, the amount of work done by an external agent in moving a charge q_o from initial point ‘i’ to final point ‘f’ in an external electric field is given by-

 

(Important)

 

From here, it may be noted that-

• The work done in moving the test charge in an electric field is independent of the path followed.
• This is because the work done depends only on the potential difference between the initial and final points.

 

Important Tip While using the above formula, always put the value of charge qo with a proper sign.

 

Read the next article on-

Relation Between Electric Field & Electric Potential

 

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