Lecture 3 Electrical Energy Chapter 16.1  16.5 Outline Potential Difference Electric Potential Equipotential Surface

Conservative Forces Both, gravitational and electric, forces acting on an object produce work. The work done is equal to the force magnitude times the distance through which the force acts. Both forces are conservative. This means that the work done by a force on an object depends only on the initial and final positions of the object and not on the path between the points. The work along a closed path is zero.

Potential Difference E  electric field magnitude The work done by the force moving the charge from A to B is W AB =qEd q  a small positive charge The charge gains kinetic energy and loses potential energy

Potential Difference The work done by a conservative force equals the negative of the change of potential energy,  PE.  PE =  W AB =  qEd (valid only for the case of a uniform field) The potential difference between points A and B is the change in potential energy of a charge q moved from A to B divided by the charge size.  V  V B  V A =  PE / q

Units of Electric Potential Difference Electric potential difference is a measure of energy per unit charge. Units of electric potential are joules per coulomb. 1 V = 1 J/C The above equation also shows that 1 N/C = 1 V/m. Both, potential energy and potential are scalars.  PE  =  V =  Ed q

Energy Change in the Electric Field The direction of the electric field is the direction of the electric force, exerted on a positive charge. Thus, a positive charge gains electrical potential energy when it is moved in a direction opposite the electric field. Similarly, a negative charge moving in a direction opposite to the electric field loses electrical potential energy. Positive charges move from a point of higher potential to a point of lower potential.

Electric Potential of a Point Charge The point of zero electric potential is defined to be at an infinite distance from the charge. q V = k e  r The potential (or work per unit charge to move a test charge from infinity to a distance r from a positive charge q) increases the closer the positive test charge is moved to q. The potential of a point charge decreases with distance as 1/r, while the electric field decreases as 1/r 2.

Electric Potential What is the potential 2 meters away from a one nano-coulomb (10  9 C) charge? V = V(r) = k e q/r k e = 9 x 10 9 (SI units) q = 1 x 10  9 C r = 2 m V = 9 x 10 9 (1 x 10  9 ) / 2 = 4.5 V

Work Due to Potential Difference How much work would be done by the electric field if Q = 20 C were moved from A to B? W =  Q  V, Q = 20 C  V = 8V  4.5 V = 3.5 V W =  (20 C) (3.5 V)=  70 J

Potential Due to 2 Charges V = k e q/r for each charge, add the potentials: V = (9 x 10 9 )(4 x 10  9 )/12 = 4 V V = (9 x 10 9 )(6 x 10  9 )/27 = 2 V Total Potential: 6 V What is the potential at Point P?

Potentials and Charged Conductors W =  q (V B – V A ) If V B – V A = 0, no work is required to move a charge between points A and B. When a conductor is in electrostatic equilibrium, a net charge resides entirely on its surface. The electric field just outside the conductor is perpendicular to the surface. The electric field inside the conductor is zero.  All points on the surface of a charged conductor in electrostatic equilibrium are at the same potential.

Surface Potential No work is done to move a charge along the conductor’s surface  the electric potential is constant everywhere on the surface. No work is required to move a charge inside the conductor  the electric potential is constant everywhere inside the conductor.

Equipotential Surfaces Equipotential surface (equipotential) is a surface on which all points are at the same potential  no work is required to move a charge at constant speed on such a surface. The electric field at every point on an equipotential surface is perpendicular to the surface.  Heart equipotential surfaces

Summary The electric potential difference between 2 points is the change in electrical potential energy of a unit charge The electric potential equals to work per unit charge to move a test charge from infinity to a certain distance from a positively charge object The electric potential is constant everywhere on the surface and inside a conductor in electrostatic equilibrium Equipotential surface is a surface on which all points are at the same potential