Conductors: External Electric Field 1/28/2018 1
Two Parallel Conducting Sheets Find the electric field to the left of the sheets, between the sheets and to the right of the sheets. 1/28/2018 2
Uniform Charge Density: Summary Cylindrical symmetry Planar Spherical symmetry Non-conductor E E E r 2 0 2 R 2 r 0 2 0 E 1 4 0 E 1 Conductor E 0 E 2 0 r E 0 Q R r 3 E 0 Q E 2 4 0 r 4 2 0 r 1/28/2018 3 1 Q inside outside inside outside
Summary of Lectures 3, 4 & 5 *Relates net flux, F, of an electric field through a closed surface to the net charge that is enclosed by the surface. F E da q o o enc *Takes advantage of certain symmetries (spherical, cylindrical, planar) *Gauss Law proves that electric fields vanish in conductor, extra charges reside on surface 1/28/2018 4
Lectures 6 & 7: Chapter 23 Electric Potential Q V 4 0 R Q 4 0 r Definitions C R R R r Examples B r B q r A A Path independence Equipotential surfaces 1/28/2018 5
From Mechanics (PHYS 172) Energy Kinetic Energy: associated with the state of motion Potential Energy: associated with the configuration of the system Conservative Forces: Work done by a conservative force is independent of path 1/28/2018 6
From Mechanics (PHYS 172) Work W DK TOT F dr W > 0 Object speeds up ( DK > 0 ) or F dr F dr W < 0 Object slows down (DK < 0 ) F dr W 0 Constant speed (DK 0 ) 1/28/2018 7
Electric Potential Energy When an electrostatic force acts between two or more charges within a system, we can assign an Electric Potential Energy: F Dx If a Coulomb force does negative work Potential energy increases 1/28/2018 8
Example: Electric Potential Energy What is the change in electrical potential energy of a released electron in the atmosphere when the electrostatic force from the near Earth s electric field (directed downward) causes the electron to move vertically upwards through a distance d? 1. DU of the electron is related to the work done on it by the electric field: 2. Work done by a constant force on a particle undergoing displacement: 3. Electrostatic Force and Electric Field are related: 1/28/2018 9
Example: Electric Potential Energy What is the change in electrical potential energy of a released electron in the atmosphere when the electrostatic force from the near Earth s electric field (directed downward) causes the electron to move vertically upwards through a distance d? 1. DU of the electron is related to the work done on it by the electric field: Key Idea: DU W 2. Work done by a constant force on a particle undergoing displacement: E F e d Key Idea: W F d 3. Electrostatic Force and Electric Field are related: Key Idea: F qe W qe d qed cos qed cos180 qed DU W qed Electric potential decreases as electron rises. 1/28/2018 10
Electric Potential versus Electrical Potential Energy Electric Potential is a property of an electric field and is measured in J/C or V Electric Potential Energy is an energy of system consisting of the charged object and the external electric field, and is measured in Joules. 1/28/2018 14
Potential & Electric Fields The electric field points in the direction in which the potential decreases most rapidly. 1/28/2018 15
Example: Potential Difference *independent of path i c (a) What is DV moving directly from point i to point f? f (b) What is DV moving from point i to point c to point f? 1/28/2018 17
Potential due to a point charge: Find V in space around a charged particle relative to the zero potential at infinity: 1/28/2018 18
V(r) versus r for a positive charge at r = 0 V(r) to kq r For a point charge r V(r 0) 1/28/2018 19
Electrical Potential Energy Push q 0 uphill and its electrical potential energy increases according to U kq 0q r The work required to move q 0 initially at rest at is W kq q 0. r Work per unit charge is V kq r. 1/28/2018 20
Demo 5A-16 R V(r) kq R R V(R) kq R Gauss law says the sphere looks like a point charge outside R. 1/28/2018 21
Demo 5A-35 DU q DV Get energy out charge flow R Also try an elongated neon bulb. V kq R r 1 r 2 DV V(r 1 ) V(r 2 ) across fluorescent light bulb 1/28/2018 22
d = 1.3 m Potential due to a Group of Point Charges Find the Potential at the center of the square. N n 1 V(r) V n (r) 1 4 o N n 1 q n r n q 1 = 12 nc q 2 = -24 nc - q 3 =31 nc q 3 =17 nc 1/28/2018 23
Electrical Potential Energy of a System of Point Charges U of a system of fixed point charges equals W done by an external agent to assemble the system by bringing each charge in from infinity. If q1 & q2 have the same sign, we must do positive work to push against mutual repulsion. If q1 & q2 have opposite signs, we must do negative work against mutual attraction 1/28/2018 25
Calculating the Electric Field from the Potential Field V V V E V iˆ ˆj kˆ x y z E points in the direction in which the potential decreases most rapidly. From this we see that V V V E, E, and E. x y z x y z 1/28/2018 26
Potential Energy of an Electric Dipole Potential energy can be associated with the orientation of an electric dipole in an electric field. p E pe sin 0 0 U W d pe sin d 90 90 U pe cos U 0 0 Choose 0( 90 ) 0 cos U U pe p E U is least =0 U=-pE U is greatest =180 U=pE U =0 when =90