Electrical Potential Energy

• Like gravity the electric force is a conservative force. Therefore it should be possible to talk about an electrical potential energy in the same way we talk about a gravitational potential energy. This is not surprising because of the similarity between symbolic structure of the gravitational force and the electrical force.
  
  
• The electrical potential energy at a given point is defined to be the negative of the of work an external force would have to do to move a charge from the location chosen as the zero reference level to the point. The negative sign come from the fact that we have moved the 'work done against the electrical force' from one side of the work energy equation to the other side to put it on an equal footing with the kinetic energy.

• The work it takes to move a point charge q in an electric field E is given by,

When we calculate the integral we will get the difference between two expressions, one evaluated at location b substracted another evaluated at location a.

The electrical potential energy at a single point is defined by

The constant C is determined by our choice of the location of the zero energy level and can not always be set equal to zero.

The potential energy at the location of a test charge q due to the E-field created by another point charge Q can be calculated

• If we choose C = 0, then the zero energy reference point is at infinity since 1/r goes to zero as r becomes large.
  
  
• The electrical potential energy of charge q due to charge Q is

• This could also be look at as the minimum amount of work required to move two charges from infinity to where they are a distance r apart by any path. Alternately, if one charge is already located at some point, the above energy represents the work needed to move the other charge from infinity to a distance r from the first charge.
  
  
• If both charge have the same sign then the PE will be positive - meaning that it would take positive work to move the charges closer together because two like charges repel each other. On the other hand, if the two charges have different signs the PE will be negative - meaning the system could work since unlike charge attract each other.

Electric Potential - Voltage