From last time(s)… Today… Gauss’ law Conductors in electrostatic equilibrium Today… Finish conductors in electrostatic equilibrium Work, energy, and (electric) potential Electric potential and charge Electric potential and electric field. Oct. 2, 2008

Exam 1 Scores Class average = 76% (This is 84/110) Your score posted at learn@uw Curve: B / BC boundary is 76% Oct. 2, 2008

Conductor in Electrostatic Equilibrium In a conductor in electrostatic equilibrium there is no net motion of charge E=0 everywhere inside the conductor Ein Conductor slab in an external field E: if E  0 free electrons would be accelerated These electrons would not be in equilibrium When the external field is applied, the electrons redistribute until they generate a field in the conductor that exactly cancels the applied field. Etot =0 Etot = E+Ein= 0 Oct. 2, 2008

Conductors: charge on surface only Choose a gaussian surface inside (as close to the surface as desired) There is no net flux through the gaussian surface (since E=0) Any net charge must reside on the surface (cannot be inside!) E=0 Oct. 2, 2008

E-Field Magnitude and Direction E-field always  surface: Parallel component of E would put force on charges Charges would accelerate This is not equilibrium Apply Gauss’s law at surface this surface this surface this surface Oct. 2, 2008

Summary of conductors everywhere inside a conductor Charge in conductor is only on the surface surface of conductor - + Oct. 2, 2008

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? + Ask what happened to the energy. v=0 v>0 Oct. 2, 2008

Work and kinetic energy Work-energy theorem: Change in kinetic energy of isolated particle = work done Total work In our case, Oct. 2, 2008

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 Ask what happened to the energy. + + Oct. 2, 2008

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. 2, 2008

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. 2, 2008

Quick Quiz Two points in space A and B have electric potential VA=20 volts and VB=100 volts. How much work does it take to move a +100µC charge from A to B? +2 mJ -20 mJ +8 mJ +100 mJ -100 mJ Oct. 2, 2008

Check for uniform E-field Push particle against E-field, or across E-field Which requires work? Constant electric potential in this direction + + Ask what happened to the energy. Increasing electric potential in this direction Decreasing electric potential in this direction Oct. 2, 2008

Potential from electric field Potential changes largest in direction of E-field. Smallest (zero) perpendicular to E-field V=Vo Oct. 2, 2008

Electric potential: general 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 Electric field usually created by some charge distribution. V(r) is electric potential of that charge distribution V has units of Joules / Coulomb = Volts Oct. 2, 2008

Electric potential of point charge Electric field from point charge Q is What is the electric potential difference? Define Then for point charge Oct. 2, 2008

Electric Potential of point charge Potential from a point charge Every point in space has a numerical value for the electric potential Distance from ‘source’ charge +Q y +Q x Oct. 2, 2008

Potential energy, forces, work Electric potential energy=qoV A B qo > 0 U=qoV Point B has greater potential energy than point A Means that work must be done to move the test charge qo from A to B. This is exactly the work to overcome the Coulomb repulsive force. Work done = qoVB-qoVA = Differential form: Oct. 2, 2008

V(r) from multiple charges Work done to move single charge near charge distribution. Other charges provide the force, q is charge of interest. q1 q2 q q3 Superposition of individual electric potentials Oct. 2, 2008

Quick Quiz 1 A B Both A and B Neither of them At what point is the electric potential zero for this electric dipole? +Q -Q x=+a x=-a A B A B Both A and B Neither of them Oct. 2, 2008

Superposition: the dipole electric potential +Q -Q x=+a x=-a Superposition of potential from +Q potential from -Q + = V in plane Oct. 2, 2008