Chapter 17 Electric Energy and Capacitance

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

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

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

Potential Difference ΔPE = - W = - q E d The potential difference between points A and B is defined as: ΔV = V B – V A = 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

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

Potentials and Charged Conductors W = -ΔPE = -q(V B – V A ), Therefore no work is required to move a charge between two points that are at the same electric potential i.e. W = 0 when V A = V B For two charges separated by r PE = k e q 1 q 2 r Charged Surfaces and Conductors All points on the surface of a charged conductor in electrostatic equilibrium are at the same potential

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 J

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

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.

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(V B – V A ),

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

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

The Xerographic Process

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

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

Capacitors with Dielectrics

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

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: Є o is the permittivity of free space; Є o =8.85 x C 2 /Nm 2 d A C o K Є 

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

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

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

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

Capacitors in Parallel (have the same voltage across them) Q 1 = C 1 ΔV Q 2 = C 2 ΔV Q 1 + Q 2 = Q tot = C 1 ΔV + C 2 ΔV = (C 1 + C 2 )ΔV  for capacitors in parallel C eq = C 1 + C 2

Capacitors in Series (have the same charge on each plate) ΔV = Q C eq ΔV tot = ΔV 1 + ΔV 2 Q = Q 1 + Q 2 C eq C 1 C 2 But Q=Q 1 = Q 2  for capacitors in series 1 = C eq C 1 C 2 Ex & 7 p. 515 C eq = C 1 C 2 C 1 + C 2

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

Chapter 15 Summary ke is called the Coulomb Constant ke = 8.99 x 109 N m2/C2 εo is the permittivity of free space and equals 8.85 x C 2 /Nm 2 Φ E = E A A is perpendicular to E

Chapter 16 Summary Q = C  V capacitors in series 1 = Ceq C1 C2 capacitors in parallel Ceq= C1+ C2.... C eq = C 1 C 2 C 1 + C 2 or d A C o K Є  Єo is the permittivity of free space; Єo =8.85 x C2/Nm2 1 F = 1 C / V PE = ke q 1 q 2 r W = -ΔPE = -q(V B – V A )