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**Unformatted text preview: **Chapter 16: Electric Energy and Capacitance Dr. G. Antar 2 Outline Electrostatic potential Potential Energy Potential Difference Work and potential energy Conductors in equilibrium Equipotential surfaces Dr. G. Antar 3 Electric Potential of a Point Charge The point of zero electric potential is taken to be at an infinite distance from the charge. The potential created by a point charge q at any distance r from the charge is: A point of zero electric charge can be set by connecting the object to Earth or in other words GROUNDING . r q k V e = Dr. G. Antar 4 Electric Field and Electric Potential Dependence on the Distance to the Charge The electric field is proportional to 1/ r 2 The electric potential is proportional to 1/ r Dr. G. Antar 5 Electric Potential of Multiple Point Charges The total electric potential at some point P due to several point charges is the algebraic sum of the electric potentials due to the individual charges The algebraic sum is used because potentials are scalar quantities Consequently, it is easier to estimate the electric potential at some point than the electric field as the sum of the latter involves vectors. ( 29 algebraic sum TOT i i V V = Dr. G. Antar 6 Electrical Potential Energy ( PE ) of Two Charges V 1 is the electric potential due to q 1 at some point P The work required to bring q 2 from infinity to P without acceleration is q 2 V 1 This work is equal to the potential energy of the two particle system r q q k V q PE e 2 1 1 2 = = Dr. G. Antar 7 Notes About Electric Potential Energy of Two Charges If the charges have the same sign, PE is positive Positive work must be done to force the two charges near one another The like charges would repel If the charges have opposite signs, PE is negative The force would be attractive Work must be done to hold back the unlike charges from accelerating as they are brought close together http://www.falstad.com/vector2de/ Play 2D The electrical potential difference is the voltage present between two points. The potential difference between points A and B is defined as the change in the potential energy (final value minus initial value) of a charge q moved from A to B divided by the size of the charge PE = q V = q ( V B V A ) Potential difference is not the same as potential energy Dr. G. Antar 8 Potential Difference Dr. G. Antar 9 Potential Difference, cont. Another way to relate the energy and the potential difference: PE = PE B - PE A = q ( V B - V A ) =q V AB Both electric potential energy and potential difference are scalar quantities Units of potential difference V = J/C A special case occurs when there is a uniform electric field V AB = V B V A = - E x Dr. G. Antar 10 Recall the Definition of WORK In physics, WORK is the amount of energy transferred by a (macroscopically measurable) force....

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