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From last time(s)…

From last time(s)…. Gauss’ law Conductors in electrostatic equilibrium. Finish conductors in electrostatic equilibrium Work, energy, and (electric) potential Electric potential and charge Electric potential and electric field. Today…. Exam 1 Scores. Class average = 76%. (This is 84/110).

samuel-hanson
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From last time(s)…

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

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

  3. 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

  4. 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

  5. this surface this surface this surface 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

  6. - - + + - + - + - - + + Summary of conductors • everywhere inside a conductor • Charge in conductor is only on the surface • surface of conductor

  7. + + 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

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

  9. + 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 +

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

  11. 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

  12. 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

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

  14. Potential from electric field • Potential changes largest in direction of E-field. • Smallest (zero) perpendicular to E-field V=Vo

  15. 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

  16. for point charge Electric potential of point charge • Electric field from point charge Q is • What is the electric potential difference? Define Then

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

  18. B Electric potential energy=qoV A qo > 0 Potential energy, forces, work • 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:

  19. 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

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

  21. x=-a x=+a +Q -Q Superposition: the dipole electric potential • Superposition of • potential from +Q • potential from -Q + = V in plane

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