Slide 1

Electric Potential

To apply conservation of energy, we need to define electric potential energy for other types of potential energy. Potential energy can only be defined for a conservative force.The work done by a conservative force in moving an object between any 2 positions is independent of the path taken. Electric Potential EnergyElectric potential energy (PE) is energy stored in the electric field.

PE depends only on the location, not upon the path taken to get there (conservative force). PE = 0 at some reference point. For two point particles take PE = 0 at r = .

For the electric force

Electric Potential EnergyThe change in U(PE) between 2 points a and b equals to the ve work done by the conservative force to move an object from a to b: PE = -WP.E=PEb PEa (the change in electric potential energy)Electric Potential EnergyFor example, consider the electric field between 2 equally but oppositely charged parallel plates and electric field, E is uniform over most of the region. Now consider a tiny +ve q placed at point very near to +ve plate. q is small and doesnt affect E. If q at point a is released, the electric force will do work on the charge and accelerate toward ve plate. Work done: W = Fd = qEd

Electric Potential Energy(when U is negative, the potential energy decrease)

Change in electric potential energy is negative of work done by electric force:

Electrostatic Potential Energy and Potential Differencewhen U is negative, the potential energy decrease.as particle charged particle accelerates from point a to point b, the particle/s kinetic energy KE increases by an equal amount.

Note that the positive charged q has its greatest potential energy at point a near the positive plate.

Electric potential, V is defined as potential energy, P.E per unit charge:If a positive test charge q has electric potential energy, PEa at some point a, the electric potential at this point is

Unit of electric potential: the volt (V).1 V = I J/CElectrostatic Potential Energy When electric force does positive Work on charge, KE increases and PE decreases. The difference in potential energy, PEb-PEa, is equal to the negative of the work, Wba by the electric field to move the charge from a to b,

(17-2b)Potential DifferenceThe positive plate is at a higher potential than the negative plate. Thus a positively charged object moves naturally from a high potential to a low potentialWork done by the electric field to move a positive charge q from a to b is equal to the negative of the change in potential energy:

Work is also force multiplied by distance:

Relation between Electric Potential and Electric FieldSolving for the field,

(17-4b)If the field is not uniform, it can be calculated at multiple points:

Relation between Electric Potential and Electric FieldWhat about the signs (+ -)?Even though potential and potential energy are scalars, the signs do have meaning:The electric field line arrows indicate the direction of force on a positive charge.The electric field lines point in the direction of decreasing potential.The electric field lines point in the direction of decreasing PE for a positive charge.Or as a + charge moves in the direction of the field lines PE decreases

An equipotential is a line or surface over which the potential is constant.Electric field lines are perpendicular to equipotentials. The surface of a conductor is an equipotential.

Equipotential Lines

Equipotential LinesThe Electron Volt, a Unit of EnergyOne electron volt (eV) is the energy gained by an electron moving through a potential difference of one volt.

The electric potential due to a point charge can be derived using calculus.

(17-5)Electric Potential Due to Point Charges

These plots show the potential due to (a) positive and (b) negative charge.Electric Potential Due to Point ChargesEXAMPLEHow much work does the electric field do in moving a proton from a point with a potential of 185 V to a point where it is 55 V?

An electron acquires 5.253 x 10-16 of kinetic energy when it is accelerated by an electric field from plate A to plate B. What is the potential difference between the plates, and which plate is at the higher potential?

The electron moves from low potential to high potential, so plate B is at the higher potentialEXAMPLEThe electric field between two parallel plates connected to a 45-V battery is 1300 V/m. How far apart are the plates?

EXAMPLE(a) What is the electric potential 0.50 x 10-10 from a proton (charge )? (b) What is the potential energy of an electron at this point?

(b)The potential energy of the electron is the charge of the electron times the electric potential due to the proton.

EXAMPLE