Chapter 17

1. Chapter 17 Electric Energy and Capacitance

2. Work and Potential Energy • For a uniform field between the two plates • As the charge moves from A to B, work is done in it • W = F d= q E d • ΔPE = - W = - q E d • only for a uniform field

3. Summary of Positive Charge Movements and Energy • When a positive charge is placed in an electric field • It moves in the direction of the field • It moves from a point of higher potential to a point of lower potential • Its electrical potential energy decreases • Its kinetic energy increases

4. Summary of Negative Charge Movements and Energy • When a negative charge is placed in an electric field • It moves opposite to the direction of the field • It moves from a point of lower potential to a point of higher potential • Its electrical potential energy decreases • Its kinetic energy increases

5. Potential Difference • ΔPE = - W = - q E d The potential difference between points A and B is defined as: • ΔV = VB – VA = ΔPE / q =-Ed • Potential difference is not the same as potential energy • 1V is defined as 1 J/C 1 Joule of work must be done to move a 1C across 1V potential difference

6. Electric Potential of a Point Charge • The point of zero electric potential is taken to be at an infinite distance from the charge • The potential created by a point charge q at any distance r from the charge is V is scalar Quantity (superposition applies) • A potential exists at some point in space whether or not there is a test charge at that point

7. Potentials and Charged Conductors • W = -ΔPE = -q(VB – VA), • Therefore no work is required to move a charge between two points that are at the same electric potential i.e. W = 0 when VA = VB • For two charges separated by r PE = ke q1q2 r Charged Surfaces and Conductors • All points on the surface of a charged conductor in electrostatic equilibrium are at the same potential

8. The Electron Volt • The electron volt (eV) is defined as the energy that an electron (or proton) gains when accelerated through a potential difference of 1 V • Electrons in normal atoms have energies of 10’s of eV • Excited electrons have energies of 1000’s of eV • High energy gamma rays have energies of millions of eV • 1 eV = 1.6 x 10-19 J

9. Equipotential Surfaces • An equipotential surface is a surface on which all points are at the same potential • No work is required to move a charge at a constant speed on an equipotential surface • The electric field at every point on an equipotential surface is perpendicular to the surface

10. Equipotential Surfaces and Their Relation to the Electric Field An equipotential surface is a surface on which the electric potential is the same everywhere. The net electric force does no work on a charge as it moves on an equipotential surface.

11. Equipotentials and Electric Fields Lines -- Positive Charge • The equipotentials for a point charge are a family of spheres centered on the point charge • The field lines are perpendicular to the electric potential at all points • W = -ΔPE = -q(VB – VA),

12. Equipotentials and Electric Fields Lines -- Dipole • Equipotential lines are shown in blue • Electric field lines are shown in red • The field lines are perpendicular to the equipotential lines at all points

13. Application – Electrostatic Precipitator • It is used to remove particulate matter from combustion gases • Reduces air pollution • Can eliminate approximately 90% by mass of the ash and dust from smoke • Application – Electrostatic Air Cleaner

14. The Xerographic Process

15. 17.2 Relation between Electric Potential and Electric Field Work is charge multiplied by potential: Work is also force multiplied by distance:

16. 17.2 Relation between Electric Potential and Electric Field Solving for the field, (17-4b)

17. Capacitors with Dielectrics

18. Capacitance • A capacitor is a device used in a variety of electric circuits—Often for energy storage • Units: Farad (F) • 1 F = 1 C / V • A Farad is very large • Often will see µF or pF

19. Parallel-Plate Capacitor • The capacitance of a device depends on the geometric arrangement of the conductors • For a parallel-plate capacitor whose plates are separated by air: Єo is the permittivity of free space; Єo =8.85 x 10-12 C2/Nm2 A K Є = C o d

20. 17.8 Dielectrics Dielectric strength is the maximum field a dielectric can experience without breaking down.

21. 17.8 Dielectrics The molecules in a dielectric tend to become oriented in a way that reduces the external field.

22. Applications of Capacitors – Camera Flash • The flash attachment on a camera uses a capacitor • A battery is used to charge the capacitor • The energy stored in the capacitor is released when the button is pushed to take a picture • The charge is delivered very quickly, illuminating the subject when more light is needed

23. Applications of Capacitors -- Computers • Computers use capacitors in many ways • Some keyboards use capacitors at the bases of the keys • When the key is pressed, the capacitor spacing decreases and the capacitance increases • The key is recognized by the change in capacitance

24. Capacitors in Parallel(have the same voltage across them) Q1 = C1ΔV Q2 = C2ΔV Q1 + Q2 = Qtot = C1ΔV + C2ΔV = (C1+ C2)ΔV  for capacitors in parallel Ceq= C1+ C2

25. Capacitors in Series(have the same charge on each plate) ΔV = Q Ceq ΔVtot = ΔV1 + ΔV2 Q = Q1 + Q2 Ceq C1 C2 But Q=Q1= Q2 for capacitors in series 1 = 1 + 1 Ceq C1 C2 Ceq = C1C2 C1 + C2 Ex. 16.6 & 7 p. 515

26. Energy Stored in a Capacitor • Energy stored = ½ Q ΔV • From the definition of capacitance, this can be rewritten in different forms Q = CV

27. Chapter 15 Summary • ke is called the Coulomb Constant • ke = 8.99 x 109 N m2/C2 • ΦE = E A A is perpendicular to E • εo is the permittivity of free space and equals 8.85 x 10-12 C2/Nm2

28. Chapter 16 Summary PE = ke q1q2 r W = -ΔPE = -q(VB – VA) 1 F = 1 C / V A K Є Єo is the permittivity of free space; Єo =8.85 x 10-12 C2/Nm2 = C o d capacitors in series 1 = 1 + 1 . . . . Ceq C1 C2 Ceq = C1C2 C1 + C2 or capacitors in parallel Ceq= C1+ C2 . . . . Q = CV