Chapter 17:Electric Forces

and Fields

Objectives

• Understand the basic properties of electric charge.

• Differentiate between conductors and insulators.

• Distinguish between charging by contact, charging by induction, and charging by polarization.

Electric Charge• protons have positive (+) charge• electrons have negative (–) charge• opposite charges attract; like charges repel• charge is always conserved (cannot be destroyed)• charge (q) is measured in coulombs (C)

Charles Augustin Coulomb1736 - 1806

Electric Charge is Quantized

qE mg

qmg

E

+

qE

mg

Charge on drop occurs in multiples of 1.60 x 10-19 C(±1e, ±2e, ±3e…).

1909: Robert Millikan

Transfer of Electric Charge

• charges move freely through conductors (typically metals)

• charges do not move freely in insulators (most other solids)

Electric charge can be transferred 3 ways:• contact• induction• polarization

Objectives

• Calculate electric force using Coulomb’s law.• Compare electric force with gravitational

force.

Coulomb’s Law

F Gm m

rG 1 22

F kq q

re 1 22

Law of Universal Gravitation

Coulomb’s Law

Compare the gravitational and the electric forces between the proton and electron in a hydrogen atom.

k = 8.99 x 109 Nm2/C2

Objectives

• Calculate electric field strength.• Draw and interpret electric field lines.• Identify the properties associated with a

conductor in electrostatic equilibrium.

Electric Fields

Field lines show direction and strength of force (represented by the line density)

• gravitational field (g)• electric field (E): (+) → (–)

F q E

EF

q

e

e

0

0

units are N/C

F m g

gF

m

g

g

Electric Fields

The nucleus applies a force of 8.16 x 10-11N on the electron in a hydrogen atom. What is the electric field strength at the position of the electron?

Electric Field due to a Point Charge

(a) What is the E-field strength at a distance of 0.45 m from a 8.2mC charge?(b) What force would be felt by a proton at this location?(c) What is the initial acceleration of the proton?

F kq q

r

EF

qkq q

r q

E kq

r

e

e

02

0

02

0

2

Conductors in Electrostatic Equilibrium

electrostatic equilibrium: no net motion of charge(a) The total electric field inside a conductor equals zero.(b) Excess charge resides on the surface.(c) E-field lines extend perpendicular to the surface.(d) Charge accumulates at points.

Chapter 18: Electric Energy

and Capacitance

Electric Potential Energy (EPE)

PE m g hgrav PE q E delectric

g

E

ME KE PE PE PEgrav elastic electric

• uniform field only!• displacement in direction of the field

EPE Problems

• What is the change in EPE if a proton is moved 2.5mm in the direction of a uniform 7.0 x1011 N/C electric field?

• What is the change in EPE if an electron is moved in the same direction?

EPE for a Pair of Charges

• Two alpha particles (two helium nuclei, 2 p+ each) have an EPE of 6.32 x10-19 J. What is the distance between the two particles?

PE q E d F r kq q

rr

PE kq q

r

elec e

elec

1 22

1 2

Potential Difference (Voltage)PE m g h

PE

mg h

grav

grav

PE q E d

PE

qE d

vo ltagePE

qE d

V E d

electric

electric

electric

" "

• voltage (V) is EPE per charge• 1 volt = 1 J/C• measured with a voltmeter or multimeter• voltage is like “electric pressure”

(uniform field only)

Voltage Problems

What voltage exists in a 3.5 x10-6 N/C electric field between two points that are 0.25 m apart?

Capacitors

• Capacitors store EPE between two closely-spaced conductors that are separated by an insulator.

• Capacitance is measured in farads (F). 1 F = 1 C/V

CQ

VPE Q Velectric

12

Chapter 19:Electric Current and

Electric Power

Electric Current

Electric charges will flow between areas of different electric potential (voltage)

• electric current (I): a flow of electric charge• 1 ampere (A) = 1 C/s• measured with an ammeter• although electrons typically flow, current is defined as direction of positive flow (+ → –)• drift speed of e– in Cu at 10 A is only 0.00025 m/s• 0.005 A is painful and 0.070 A can kill you

Electric Resistance

• resistance (R): resistance to electron flow• measured in Ohms (Ω)• V ↑, I ↑• R ↑, I ↓

IV

R

A 2400-Ω resistor is attached to a 12-V power source. What is the current through the wire?

AC/DC• alternating current: electric field reverses periodically, current alternates direction (60 hz in USA)

• direct current: field is constant, current is constant• batteries produce DC• electric generators can make AC or DC

Electric Power and Energy

J

CV

J C V

J

s

C V

s

C

sV

W A V

P I Velec

Consider the units of voltage:

E I V telec

Power Problems

If voltage = 120 V, what is the current through a 1200-W hairdryer?

At $0.05 / kW·hr, how much does it cost to operate a 240-W television for 24 hrs?