Potential Energy due to charge

     Concept of Potential Energy      

The potential energy arises due to system of charges. Two charges placed in its vicinity exert a electrostatic force according to coulomb's law. Thus work need to be done in order to move a charge in presence of other charges. This work done is stored as potential energy of the system. The work done against the electrostatics force is stored as potential energy of the system. This work done increases the potential energy of the system. Since any system tries to achieve minimum energy level configuration , work is suppose to be done in order to change the configuration. 

dU = F_E. ds

where dU is change in potential energy of the system.

 F_E is the electrostatic force applied on charge.

ds is the displacement of the charge.

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Expression for potential energy of a charged system

Let a charge  +Q is placed at a point  M which creates electrostatic field around. Let a charge q₀ is palced at point O. This charge is moved from point O to N at a distance r₁ and r₂ from M respectively.The work done in displacing the charge against electrostatic field is given by

dU = F_E. ds = -F_E. ds

Negative sign  is due to work done against electrostatic field.

Thus the change in potential energy  ΔU is obtained  by integrating dU.

We know the electrostatic force is given by,

The above equation gives expression for potential energy which is equivalent to work done and is independent on actual path travel

At infinity the electrostatic force is zero .Thus the equation changes to 

Let understand it via a short video 

When  a positive charge is brought near a test charge towards left a shown ,the change in potential energy leads to increase in potential energy of the system

When  a negative charge is brought near a test charge towards left a shown ,the change in potential energy leads to decrease in potential energy of the system

_{Previous: Electrostatics}

Next: Potential 

  

              

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