1. Electric Energy

2. Electrical Potential Energy  Potential energy is the negative of the work done by conservative forces. Potential energy  U =  W conPotential energy  U =  W con  Electrical work is done by the Coulomb force. Electrical potential energyElectrical potential energy

3. Changing State  A charge in an electric field is subject to a force.  Moving the charge against the field requires work.  The state of the charge is changed to increase the potential energy. q q d F E

4. Potential Difference  The potential energy is expressed as a difference of the energy of two states.  The electric potential can be expressed with respect to a test charge. q q d F E UU

5. Point Potential  Coulomb’s law is mathematically similar to gravitational force. Define potential energy similarlyDefine potential energy similarly Point charge QPoint charge Q Test charge qTest charge q  Apply the definition of the electric potential.  Like gravity zero is at infinity.

6. Potential Curve  The point potential can be attractive or repulsive. Attraction like gravityAttraction like gravity

7. Arbitrary Zero  The zero of potential energy is arbitrary.  U can be defined, but  U is what really matters. Compare energy to workCompare energy to work  We can measure the change in electric potential V. No experiment reveals the specific valueNo experiment reveals the specific value E V = 0 q VfVf

8. Charge Energy  The electric force is conservative. Energy is conservedEnergy is conserved Independent of the experimentIndependent of the experiment  Suppose that charge were not conserved. An experiment would be able to cause some charge to vanishAn experiment would be able to cause some charge to vanish Loss of specific amount of potential energyLoss of specific amount of potential energy Inconsistent with energy conservationInconsistent with energy conservation E V = 0 q VfVf

9. Conservation of Charge  The arbitrary zero of the potential was the heart of the preceding contradiction.  To have an electric potential independent of the choice of zero, and be conservative, requires charge conservation.  This is an example of symmetry in physics. next