Electric potential

and capacitance

 

Electric potential energy is denoted as U.



 1)Suppose Q is a source charge.


2) q is a test charge


3) Now the definition.

Electrostatic potential energy of charge q at a position in an electric field is defined as the work done by an external force on brining the charge q from infinity to that position without any acceleration.



4)Here Q is the source charge.


5)A test charge q is brining from infinity to the position A.


6) As charge Q was already there. work and force must apply to bring the charge to the position A.


7) This work done or energy will be stored on the charge q at that position A, and this energy is called potential energy of the charge q at position A.


8)Potential energy difference between any point A and B is




Electrostatic Potential

difference 


 

1)Electrostatic potential difference between two points A & B in an electric field is defined as the work done in carrying a unit positive charge from the position A to the position B without any acceleration.


Path independent

 

2)Suppose there is an electric field of strength E, A unit positive charge is carrying from A to B as shown in the diagram through two path way Y & Z.


3) This carrying is followed by without any acceleration


4)No matter which pathway you choose it may be Y path or Z path, the work done is same, the potential difference 

is

 


Where VB  = is the potential at B

VA  = is the potential at A