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Electricity Electric Potential Review of Work Work Done on a Point Charge by a Point Charge Potential Energy and Potential of Point Charges Potential Energy and Potential of Many Point Charges Relationship between Force, Field, Energy, Potential Potential Surfaces SI Units Field and Potential Graphs 1 Electric Power Electricity Electric Potential Definition of Work Work is defined as the amount of force acting over a distance. The unit of work is either Joules (J) or electron-volts (eV) Δr F φ W F r W F r cos 2 Electricity Electric Potential Example of Work W F r The following is an example of the work done by gravity on a mass. y Δw Δh1 x m Δh2 W mgh1 0 mgh2 mgh1 0 mgh2 3 Electricity Electric Potential Example of Work W F r This is an example using the the fact that integrals are areas under a curve. F (N) 1 A1 0 -1 A2 0 4 1 X (m) 2 1 1 A1 bh 5m 2 N 5 J 2 2 1 1 A2 bh 3m 4 N 6 J 2 2 W A1 A2 1J Electricity Electric Potential Definition of a Conservative Force A force is conservative if the work it does on an object is zero when the object moves along a path and returns to its initial position. Examples of conservative forces are gravity, elastic force, electricity and magnetism. The following are not conservative: friction, tension, normal force. 5 Electricity Electric Potential Example of a Conservative Force Gravity as a mass is raised and lowered y Δh1 W1 mgh1 2 W2 0 1 x m Δh2 W4 0 5 4 6 3 W3 mgh2 mgh1 W5 mgh2 WTOTAL = 0 Electricity Electric Potential Example of a Non-conservative Force Friction on a block that is moving around a table y ΔL1 2 W1 f s L1 W2 f s w 1 x m ΔL2 3 W3 f s L2 L1 W4 f s w 5 4 W5 f s L2 Δw 7 WTOTAL = - fs (2ΔL1 + 2ΔL2 + 2Δw ) Electricity Electric Potential Consider the work necessary to put together two point charges. The force is given by Coulomb’s Law. kq1q2 F r12 2 The work needed to bring one charge from infinity to within a distance r12 of the other is W r12 kq1q2 kq1q2 dr r2 r r12 kq1q2 r12 Don’t worry about the integral in the last equation. It is only there so that those who know calculus can see where the other part came from. 8 Electricity Electric Potential The potential energy held between these two point charges is then kq1q2 U W r12 Now we consider the same relationship, but with electric field instead of force. This we call the potential. U F r V E r Since F q,Ethen we see that U qV 9 kq V r Electricity Electric Potential What if there are more point charges? 1 U12 k q1q2 r12 qq U13 k 1 3 r13 U 23 k 2 q2 q3 r23 3 U U12 U13 U 23 k 10 qq qq q1q2 k 1 3 k 2 3 r12 r13 r23 qi q j 1 U k 2 i j rij Electricity Electric Potential 2nC Example 1 3nC 2m 2 2.1m 2.1m 3 4nC qi q j 1 1 qq qq q q q q q q q q U k k 1 2 1 3 2 1 2 3 3 1 3 2 2 i j rij 2 r12 r13 r21 r23 r31 r32 qq qq q q qq qq 1 qq U k 2 1 2 2 1 3 2 2 3 k 1 2 1 3 2 3 2 r12 r13 r23 r13 r23 r12 Nm2 2nC 3nC 2nC 4nC 3nC 4nC U 8.99 10 2 C 2m 2.1m 2.1m 9 11 Electricity Electric Potential What about potential? 1 q V10 k 1 r10 2 P0 V30 k V20 k q2 r20 q3 r30 3 q3 q1 q2 V V10 V20 V30 k k k r10 r20 r30 12 Electricity Electric Potential 2nC Example 1 3nC 2m 2 P0 2m 2m 3 4nC V0 k 13 qi q q q k 1 2 3 ri 0 r10 r20 r30 2 Nm 2nC 3nC 4nC V 8.99 109 2 C 2 2 2 3 m 3 m 3 m Electricity Electric Potential Relationship between Work, Potential Energy, Force and Potential The table below represents the fundamental equations of electricity all of which a derived from the electric field E. Quantity General Equation Ek Electric Field Force Potential Potential 14 Equation for Point Charges q1q2 F12 k 2 r12 F qE V E r q r2 U F r qV V k U12 k q r q1q2 r12 Electricity Electric Potential A surface is an equipotential surface if the electric potential at every point on the surface is the same. As charges move on an equipotential surface the electric force does no work. The electric field at a point is always perpendicular to the equipotential surface on which the point lies. The electric field always points in the direction of decreasing potential. Java Applet This Applet can be found at http://www.slcc.edu/schools/hum_sci/physics/tutor/2220/e_fields/java/ 15 Electricity Electric Potential Common SI Units in Electricity Electric Potential Electric Field Energy or Work 16 V J/C V/m N/C eV J Electricity Electric Potential Relationship Electric Potential and Electric Field The electric field is the slope of the electric potential. slope of this line is -E V s 17 Electricity Electric Potential Relationship Electric Potential and Electric Field The electric potential is the area under the curve of electric field. positive area E s negative area 18 Electricity Electric Potential What is electric power? Power is the change in work over time U qV q P V IV t t t We will use this latter when we reach the topic in circuits. 19 Electricity Electric Potential What is electric power? Power is the change in work over time U qV q P V IV t t t We will use this latter when we reach the topic in circuits. 20