1. Fields and Conductors
Actually make sense

2. Internal charge +q

3. Internal charge +q

4. Hollow conductor +q

5. Hollow conductor Inside: field from point charge +q +q –q
Between: zero field
Outside: field from point charge +q

6. Infinite thick conducting plate+
Surface charge density s
Compare field to
infinite thin sheet

7. CPS Question +
Near the plate, the field will be the same as near a thin sheet with surface charge density s.
True
False

8. another useful concept
Electric Potential
another useful concept

9. Electrical work A field does work when it moves a charge. Dx
Work done by field =  F·dx = qEDx along a uniform field

10. Electrical work
Charge has different potential energy at different locations Dx
–DU = Work done by field =  qE·dx
Potential energy is proportional to charge

11. Potential energy of two charges
Work done by field as charges separate to infinity r q1 q2
Or, outside work done to bring charges together from infinity

12. Potential energy, more charges
Field generated by several charges q1 q2 r1 r2 q3 r3 Q

13. Question The potential energy of Q in this field is: r1 r2 r3 Q
The sum of its U’s with q1 + q2 + q3
There is interference between source charges q1 q2 r1 r2 q3 r3 Q

14. U of charge assembly Strategy: bring charges together one-by-one q1 q3

15. U of charge assembly Strategy: bring charges together one-by-one q1 q3

16. Question The potential energy of the entire set of charges:
Is greater than the sum of potential energies of each charge in the field of the others
Is equal to the sum of individual energies
Is less than the sum of individual energies

17. Electric Potential V Potential energy per unit charge V = U/q
Depends on position
Property of position
Scalar quantity
Unit = J/C = V = volt

18. Electric Potential Field:force as potential:potential energy
Field is force per charge
Potential is potential energy per charge
Unit = J/C = volt = V

19. Electric Potential V DU = Ufinal – Uinitial = – qE·dx
DV = Vfinal – Vinitial = – E·dx
DU is the path integral of force
DV us the path integral of field

20. Electric field is conservative
DV from a to b is the same for all paths b a

21. Electric Potential

22. Potential and Field
Equipotential surfaces are always perpendicular to electric field lines/vectors. Why?
Potential changes rapidly where field is strong. Why?
It makes sense from the relationships between
Electric field and electric force
Electric potential and electric potential energy
Work and potential energy
Force and work

23. Question
An infinite, uniformly positively-charged plane produces a uniform electric field. How does the electric potential change with increasing distance from the plane?
Potential increases.
Potential decreases.
Potential is uniform. + x

24. Potential from a point pharge
Convention: V = 0 at R =  
So, V(r) =  E·dR r R q

25. Potential difference b
Va –Vb =  E·dR a a
DV = ? q b
Va –Vb

26. The Electron Volt eV Unit of energy
eV = (Elementary charge e) · 1 volt
Compare to Joule = (1 C)(1 V)
e = 1.60210–19 C, so eV = 1.60210–19 J

27. Board Question
An infinite, uniformly positively-charged plane produces a uniform electric field. If the potential is V(d) a distance d from the plate, what is the potential at distance d + Dx?
V(d) = Ed, so E = V(d)/d and V(d + x) = E(d + x) = V(d)(d+x)/d
V(d) + d

28. Board Question
An infinite, uniformly positively-charged line produces a radial electric field. If the potential is V(d) a distance d from the wire, what is the potential at infinite distance?
V(d) + d