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Chapter 23 Electric Potential • When a charged particle moves in an electric field, the field exerts a force that can do work on the particle. • Just as gravitational potential energy depends upon the height of the mass above the earth’s surface, electric potential energy depends upon on the position of the charged particle in the electric field. Chapter 23 1 Potential and Kinetic Energy Work done by a Force on a particle that moves from point a to point b. Potential and Kinetic Energy K=Kinetic Energy U= Potential Energy Chapter 23 2 Electric Potential Energy (joules) Electric Potential Energy in a Uniform Electric Field b b Wab F dl F cos dl a a F q0 E Wab Fd q0 Ed (Uniform electric field) where Ua is the potential energy at point a and Ub is the potential energy at point b. Chapter 23 3 Electric Potential Energy Figure 23-3 Chapter 23 4 Electric Potential Energy Figure 23-4 Chapter 23 5 Electric Potential Energy Electric potential energy distance r away from a point charge rb rb rb ra ra Wa b Fr dr Fr cos dr Fr dr ra qq0 qq0 1 1 (23-8) Fr dr dr 2 40 r 40 ra rb ra ra rb Wab Wab rb 1 qq0 1 qq0 1 U a U b 40 ra 40 rb joules where Ua = potential energy at point a and Ub = potential energy at point b As rb Wa qq0 1 U a = Potential energy of q0 40 ra between point a and Figure 23-5 infinity. where U is the potential energy of q0 at any distance r away from a point charge q. Chapter 23 6 Electric Potential Energy is path independent Figure 23-5 cos dl dr rb rb rb ra ra Wa b Fr dl Fr cos dl Fr dr ra Chapter 23 7 Electric Potential Energy Electric potential energy distance r away from many point charges The total potential energy is the algebraic sum of the individual charge energy q0 q1 q0 q2 q0 q3 q0 Ua 40 r1 40 r2 40 r3 40 Chapter 23 q1 q2 q3 r2 r3 r1 8 Electric Potential (Voltage) = Potential Energy per unit charge Wab a b Vab F Definition E · · q0 +q 0 1 volt = 1 joule/coulomb = J/C Vab Va Wab U a U b U a U b Va Vb q0 q0 q0 q0 Ua q0 Vb volts b Ub q0 Wab q0Vab volts Note: 1 ev = (1.6 x 10-19) joules b Wab F dl q0 E dl a Vab W 1 ab q0 q0 a b q joules b 0 E dl E dl a a Chapter 23 9 Electric Potential (Voltage) Electric potential distance r away from a point charge qq0 Ua 40 ra 1 Ua 1 q Va q0 40 ra Ub qq0 40 rb 1 Ub 1 q Vb q0 40 rb Vab Va Vb Figure 23-5 Chapter 23 10 Electric Potential (Voltage) Electric potential distance r away from many point charges The total Electric Potential is the algebraic sum of the individual potentials Ua q3 q1 q2 1 q1 q2 q3 Va q0 40 r1 40 r2 40 r3 40 r1 r2 r3 Chapter 23 11 Electric Potential (Voltage) Example 23-4 q1 = q2 = 12 nC Figure 23-13 Chapter 23 12 Electric Potential (Voltage) Example 23-7 K a U a Kb U b 0 U a Kb U b Kb U a U b 1 2 K b mvb q0 (Va Vb ) q0Vab 2 U a q0Va U b q0Vb U a U b q0Va q0Vb q0 (Va Vb ) Chapter 23 vb 2q0 (Va Vb ) m 13 A Charged Conducting Sphere – Electric Field and Electric Potential Inside the sphere E = 0 every where Inside the sphere V is the same every where ( assume a point charge q) b Vab Figure 23-17 Chapter 23 E dl a 14 Ionization and Corona Discharge For air to be ionized at the surface of the sphere E > 3 x 106 V/m What is V at the surface? p.795 Chapter 23 15 Calculating Electric Potential Example 23-9 Oppositely Charged Parallel Plates Uniform Electric Field b b a a Vab E dl E cos dl Ed From section 22.4 coul/m2 charge 0 0E 0Vab / d E Vab = Ed Figure 23-18 A way of measuring charge density coul/m2 charge Chapter 23 16 Calculating Electric Potential Example 23-10 Difference in Potential between two points outside an Infinite Line Charge or Charged Conducting Cylinder. b a 1 Er 20 r Vab E dl E cos dl Er dr 20 a a r b b rb a Vab rb ln 20 ra Chapter 23 rb dr r r a 17 Equipotential Surfaces (Chapter 23, Sec 4) · l a E · b Equipotential surface (always perpendicular to E) b b a a Vab E dl E cos dl 90 cos 0 Vab Va Vb 0 Va Vb Chapter 23 18 Equipotential Surfaces Figure 23-23 Chapter 23 19 Equipotential Surfaces Equipotential Surfaces and Conductors Figure 23-25 E parallel = 0. Therefore, E is perpendicular to the surface. This makes the surface of the conductor an equipotential surface. Chapter 23 20 Potential Gradient (Chapter 23, Sec 5) a b · E · If cos = 1 ( = 0o) b b b a a a b a b a Vab E dl E cos dl Edl Vab dV dV b b a a dV Edl dV Edl E dV dl potential gradient Chapter 23 21 Chapter 23 22 Chapter 23 23