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)

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.

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.

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.

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.

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 = +1.35 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.

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

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

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.

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.

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.

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.

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:

CONCLUSION: Chapter 20 Electric Potential