Chapter 17

Electric Energyand

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 dThe 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

across1V 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

r

qkV e

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 rPE = ke q1q2

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 10-19 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.

r

kqV

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(VB – VA),

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

V

QC

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

d

AC 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)

Q1 = C1ΔV Q2 = C2ΔV

Q1 + Q2 = Qtot = C1ΔV + C2ΔV

= (C1+ C2)ΔV

for capacitors in parallel Ceq= C1+ C2

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 + 1Ceq C1 C2 Ex. 16.6 & 7 p. 515

Ceq = C1C2

C1 + C2

Energy Stored in a Capacitor Energy stored = ½ Q ΔV From the definition of capacitance,

this can be rewritten in different forms

C2

QVC

2

1VQ

2

1Energy

22

Q = CV

Chapter 15 Summary

2r

Qk

q

FE e

o

2

21e r

qqkF

ke is called the Coulomb Constantke = 8.99 x 109 N m2/C2

εo is the permittivity of free space and equals 8.85 x 10-12 C2/Nm2o

E

Q

ΦE = E A A is perpendicular to E

Chapter 16 Summary

V

QC

C2

QVC

2

1VQ

2

1Energy

22

Q = CV

capacitors in series 1 = 1 + 1 . . . . Ceq C1 C2

capacitors in parallel Ceq= C1+ C2 . . . .

Ceq = C1C2

C1 + C2

or

d

AC oK Є

Єo is the permittivity of free space; Єo =8.85 x 10-12 C2/Nm2

1 F = 1 C / V

r

qkV ePE = ke q1q2

r W = -ΔPE = -q(VB – VA)