1. Review: Work and Energy
Work is defined as the product of displacement d and a parallel applied force F.
Work = Fd; Units: 1 J = 1 N m
Potential Energy U is defined as the ability to do work by virtue of position or condition. (Joules)
Kinetic Energy K is defined as the ability to do work by virtue of motion (velocity). (Also in joules)

2. Signs for Work and Energy
Work (Fd) is positive if an applied force F is in the same direction as the displacement d.
The force F does positive work. A B
The force mg does negative work. m F d
The P.E. at B relative to A is positive because the field can do positive work if m is released. mg
P.E. at A relative to B is negative; outside force needed to move m.

3. Gravitational Work and Energy
Consider work against g to move m from A to B, a vertical height h. A B m F h
Work = Fh = mgh mg g
At level B, the potential energy U is:
U = mgh (gravitational)
The external force does positive work; the gravity g does negative work.
The external force F against the g-field increases the potential energy. If released the field gives work back.

4. Electrical Work and Energy
An external force F moves +q from A to B against the field force qE. B A d Fe
Work = Fd = (qE)d + +q
At level B, the potential energy U is: qE E
U = qEd (Electrical)
The E-field does negative work; External force does positive work.
The external force F against the E-field increases the potential energy. If released the field gives work back.

5. Work and Negative Charges
Suppose a negative charge –q is moved against E from A to B. B A d
Work by E = qEd qE -q
At A, the potential energy U is: E
U = qEd (Electrical)
No external force is required !
The E-field does positive work on –q decreasing the potential energy. If released from B nothing happens.

6. Signs for Potential Energy
Consider Points A, B, and C.
+6 mC +Q A
8 cm B C
12 cm
4 cm
For +2 nC at A: U = mJ
If +2 nC moves from A to B, does field E do + or – work? Does P.E. increase or decrease?
Questions:
+2 nC
Moving positive q
The field E does positive work, the P.E. decreases.
If +2 nC moves from A to C (closer to +Q), the field E does negative work and P.E. increases.

7. The field E exist independently of the charge q and is found from:
Properties of Space
An electric field is a property of space allowing prediction of the force on a charge at that point. E
Electric Field + Q . r
The field E exist independently of the charge q and is found from:
E is a Vector

8. Electric Potential Electric Potential:
Electric potential is another property of space allowing us to predict the P.E. of any charge q at a point.
Potential + Q . r P
Electric Potential:
The units are: joules per coulomb (J/C)
For example, if the potential is 400 J/C at point P, a –2 nC charge at that point would have P.E. :
U = qV = (-2 x 10-9C)(400 J/C);
U = -800 nJ

9. The SI Unit of Potential (Volt)
From the definition of electric potential as P.E. per unit charge, we see that the unit must be J/C. We redefine this unit as the volt (V).
A potential of one volt at a given point means that a charge of one coulomb placed at that point will experience a potential energy of one joule.

10. The SI Unit of Potential (Volt)
From the definition of electric potential as P.E. per unit charge, we see that the unit must be J/C. We redefine this unit as the volt (V).
A potential of one volt at a given point means that a charge of one coulomb placed at that point will experience a potential energy of one joule.

11. Potential Difference
The potential difference between two points A and B is the work per unit positive charge done by electric forces in moving a small test charge from the point of higher potential to the point of lower potential.
Potential Difference: VAB = VA - VB
WorkAB = q(VA – VB) Work BY E-field
The positive and negative signs of the charges may be used mathematically to give appropriate signs.

12. Parallel Plates
Consider Two parallel plates of equal and opposite charge, a distance d apart. VA VB E +q
F = qE
Constant E field: F = qE
Work = Fd = (qE)d
Also, Work = q(VA – VB)
So that: qVAB = qEd and
VAB = Ed
The potential difference between two oppositely charged parallel plates is the product of E and d.

13. Summary of Formulas Electric Potential Energy and Potential
Electric Potential Near Multiple charges:
WorkAB = q(VA – VB) Work BY E-field
Oppositely Charged Parallel Plates:

14. CONCLUSION: Chapter 20 Electric Potential