From Last Time: Electric field of a single charge Electric field from multiple charges Superposition Ex: calculate electric field of dipole Oct. 1, 2009Physics 208 Lecture 91 Today: Continuous charge distributions Electric field of line, ring, plane Conductors : electrostatic equilibrium Electrostatic potential

Exam 1 results Average = 66% Curve Ave at B/BC boundary Contributes to course grade as curved score. Exams returned in Monday discussion Oct. 1, 2009Physics 208 Lecture 92 A AB B BC C D F

From Last Time: Electric field of a single charge Electric field from multiple charges Superposition Ex: calculate electric field of dipole Oct. 1, 2009Physics 208 Lecture 93 Today: Continuous charge distributions Electric field of line, ring, plane Conductors : electrostatic equilibrium Electrostatic potential

Oct. 1, 2009Physics 208 Lecture 94 Charge Densities Volume charge density: when a charge is distributed evenly throughout a volume  = Q / V dq =  dV Surface charge density: when a charge is distributed evenly over a surface area  = Q / A dq =  dA Linear charge density: when a charge is distributed along a line = Q / dq = d

Oct. 1, 2009Physics 208 Lecture 95 Infinite line of charge An infinite line of charge has a uniform charge density Coulombs / meter. What direction is the electric field at point x? x A. B. C. D. E.

Oct. 1, 2009Physics 208 Lecture 96 E-field: infinite line of charge Charge density  Coulombs/meter y r x

Oct. 1, 2009Physics 208 Lecture 97 Add all these up Units?

Oct. 1, 2009Physics 208 Lecture 98 Non-infinite (finite) line of charge What direction is the E-field above the end of the line charge? A B C D E

Oct. 1, 2009Physics 208 Lecture 99 Ring of uniform positive charge y x z Which is the graph of on the z-axis? A) B) C) D) E) z

Oct. 1, 2009Physics 208 Lecture 910 Quick quiz We have an infinite sheet of charge of uniform charge density . The electric field A.increases with distance from plane B.decreases with distance from plane C.is independent of distance from plane D.changes direction with distance from plane

Oct. 1, 2009Physics 208 Lecture 911 E-field of plane of charge Text does this as adding up rings of charge. Surface charge density

Oct. 1, 2009Physics 208 Lecture 912 Electric fields and forces Original definite of E-field was (Coulomb Force) / charge E-field produced force on charged particle.

Oct. 1, 2009Physics 208 Lecture 913 Force on charged particle Electric field produces force qE on charged particle Force produces an acceleration a = F E / m Uniform E-field (direction & magnitude) produces constant acceleration Positive charge accelerates in direction of the field Negative charge accelerates in direction opposite the electric field

Oct. 1, 2009Physics 208 Lecture 914 Motion of charged particle If no other forces, positive charge accelerates in direction of E-field. But many systems have drag forces (e.g. molecules in a liquid, etc) Drag force is complex, but usually depends on velocity. Particle reaches terminal velocity, determined by force balance

Oct. 1, 2009Physics 208 Lecture 915 Application: Gel Electrophoresis Charged macromolecules in ‘gel’ with applied E-field Electric force: F E = qE Drag force: F D ~ -cv v = qE / c Speed depends on charge and drag (molecule size) Sometimes too complex to interpret Protein electrophoresis: soak in detergent to give proteins all the same charge density. Result, small proteins move faster Steady state: F E +F D =0

Oct. 1, Conductors: electrostatic equilibrium Because charges are mobile in conductor : E-field inside conductor = 0 Non-zero E-field causes charges to move Stop at surface, generate canceling E-field Local net charge resides at surface Repulsive force between charges pushes them away from each other – stop at surface E-field at locally perpendicular to surface A parallel component would cause charge motion Has magnitude Surface charge density

Oct. 1, 2009Physics 208 Lecture 9 17 Charge distribution on conductor What charge is induced on sphere to make zero electric field? +

18 Electrogenic fish Dipole + nearby conducting object Some fish generate charge separation - electric dipole. Dipole is induced in nearby (conducting) fish Small changes detected by fish.

Oct. 1, Summary of conductors everywhere inside a conductor Charge in conductor is only on the surface surface of conductor

Oct. 1, Electric forces, work, and energy Consider positive particle charge q, mass m at rest in uniform electric field E Force on particle from field Opposite force on particle from hand Let particle go - it moves a distance d How much work was done on particle? How fast is particle moving? ++ v=0 v>0

Oct. 1, Work and kinetic energy Work-energy theorem: Change in kinetic energy of isolated particle = work done Total work In our case,

Oct. 1, Electric forces, work, and energy Same particle, but don’t let go How much force does hand apply? Move particle distance d, keep speed ~0 How much work is done by hand on particle? What is change in K.E. of particle? + + Conservation of energy?W stored in field as potential energy

Oct. 1, Work, KE, and potential energy If particle is not isolated, Work done on system Change in kinetic energy Change in electric potential energy Works for constant electric field if Only electric potential energy difference Sometimes a reference point is chosen E.g. Then for uniform electric field

Oct. 1, Electric potential V Electric potential difference  V is the electric potential energy / unit charge =  U/q For uniform electric field, This is only valid for a uniform electric field

Oct. 1, Quick Quiz Two points in space A and B have electric potential V A =20 volts and V B =100 volts. How much work does it take to move a +100µC charge from A to B? A.+2 mJ B.-20 mJ C.+8 mJ D.+100 mJ E.-100 mJ

Oct. 1, Check for uniform E-field + + Push particle against E-field, or across E-field Which requires work? Constant electric potential in this direction Decreasing electric potential in this direction Increasing electric potential in this direction

Oct. 1, Potential from electric field Potential changes largest in direction of E-field. Smallest (zero) perpendicular to E-field V=VoV=Vo

Oct. 1, Electric potential: general Electric field usually created by some charge distribution. V(r) is electric potential of that charge distribution V has units of Joules / Coulomb = Volts Electric potential energy difference  U proportional to charge q that work is done on Electric potential difference Depends only on charges that create E-fields

Oct. 1, Electric potential of point charge Electric field from point charge Q is What is the electric potential difference? Define for point charge Then

Oct. 1, Electric Field and equipotential lines for + and - point charges The E lines are directed away from the source charge A positive test charge would be repelled away from the positive source charge The E lines are directed toward the source charge A positive test charge would be attracted toward the negative source charge Blue dashed lines are equipotential