Properties of Electric Charges• There are 2 kinds of electric charge: positive (+) and

negative (–)– Carrier of positive charge in matter is the proton

(charge = +e)– Carrier of negative charge in matter is the electron

(charge = –e)– e = 1.602 10–19 C (typical “shock” experienced on a dry

day transfers about 1 10–9 C)– Charge is quantized (only comes in integer multiples of e)

• An object becomes electrically charged through transfer of negative charge (movement of electrons)– Protons don’t move because they are tightly bound to

atomic nuclei– Charge is conserved– Neutral objects have equal amounts of + and – charge

Properties of Electric Charges• Rubbing a rubber rod with wool transfers negative

charge to rod– Wool has excess positive charge due to loss of negative

charge

• Rubbing a glass rod with silk transfers negative charge to silk– Glass rod has excess positive charge

• Experiments show that:– Negatively charged rubber rod is attracted to positively

charged glass rod– Negatively charged rubber rod is repelled by another

negatively charged rubber rod

• Opposite charges attract, like charges repel

Conducting Properties of Materials• Insulators are materials in which electric charge

does not move easily– They can be charged, but charge doesn’t move well– Glass, rubber, plastic, wood, and paper are examples

• Conductors are materials in which electric charge moves easily– When an area becomes charged, charge distributes itself

over entire surface– Copper, aluminum, and silver are examples– Charge will remain on conductor if you hold it with an

insulator

• Semiconductors are materials that have electrical properties somewhere between conductors and insulators– Silicon and germanium are examples

Methods of Charging/Discharging• Charging by rubbing

– Increases surface area of contact and enhances charge transfer

– Works for insulators but not for conductors

• Charging by conduction– Charged object brought in contact with a neutral object – Neutral object becomes charged with same sign of charge

as object doing the charging – Works when (originally) neutral object is insulated

• Discharging by grounding– Negative charge leaves (or enters) object through

conducting path to Earth or other limitless reservoir of charge

– Third opening of electrical outlets is the ground (connected to ground by wire and prevents static charge from building)

Methods of Charging• Charging by induction (no contact)

– Repulsive force between like charges in charged rod and (insulated) neutral conducting sphere causes redistribution of charge on sphere (figure (b))

– Opposite (like) charges move closer to (farther from) each other

– Rod would attract sphere– Induced charge on sphere can remain

if some electrons leave through grounding– + charge becomes equally distributed

because of high mobility of remaining electrons

• In insulators, induced surface charges can occur due to polarization (alignment of molecular charge)

Application: Photocopiers

(from College Physics, Giambattista et al.)

Coulomb’s Law• The strength (magnitude) of the attractive or

repulsive force that exists between 2 stationary charged particles is given by Coulomb’s Law– |q1| and |q2| are the magnitudes of the charges

– ke = constant = 8.99 109 Nm2 / C2

– Applies only to point charges and spherical distributions of charges

• The direction of the force is always along a line joining the 2 charges– Forces are attractive or repulsive depending

on the sign (+ or –) of the charges involved – In agreement with Newton’s 3rd Law: Force

on one charge is equal in magnitude but opposite in direction to force on other charge

221

r

qqkF e

Coulomb's Law

CQ 1: Two particles are held in equilibrium by the gravitational and electrostatic forces between them. Particle A has mass ma and charge qa. Particle B has mass mb and charge qb. The distance between the charges is d. Which of the following changes will cause the charges to accelerate towards one another?

A) ma is doubled and mb is doubled.

B) ma is doubled and mb is halved.

C) qa is doubled and qb is doubled.D) d is doubled.

CQ 2: Interactive Example Problem:The Heart as an Electric Dipole

(ActivPhysics Online Exercise #11.3, copyright Addison Wesley publishing)

What is the net electric force exerted by the dipole charges on Q3 = +3.0 × 10–8 C above the dipole?

A) 0 N B) 1.3 × 10–5 N to the right

C) 1.3 × 10–5 N upD) 1.45 × 10–5 N to the right

The Electric Field• The influence of gravity on a mass m by another

mass M can be thought of as m immersed in a gravitational field due to M– We can “map” the field by keeping

track of the direction and magnitude of g at all points

– It is a vector field since it depends on magnitude & direction– The gravitational field can be written as:

• Similarly, the influence of the electrostatic force on a “test” charge +q0 by another charge Q can be described by an electric field– Field “mapped” by direction and magnitude

of E– Also a vector field– Electric field can be written as:

M mg

mg

m

Fg g

0q

FE e

The Electric Field• The direction of E at a point is the

direction of electrostatic force that would be exerted on charge +q0 at that point

• Knowing E at some point, we can calculate Fe on any charge q0 at that same point from

• Since we know the magnitude of Fe from Coulomb’s Law, the magnitude of E is given by– Magnitude of E due to charge q at

position of q0

– Direction of E depends on sign (+ or –) of source charge q (consistent with above definition)

EqFe

0

220

0

0 r

qk

rq

qqk

q

FE ee

e

Mapping Electric Fields

Example Problem #15.29

Solution (details given in class):

0tot E

30°

E1E2

E3

Three identical charges (q = –5.0 C) lie along a circle of radius 2.0 m at angles of 30°, 150°, and 270°, as shown. What is the resultant electric field at the center of the circle?

Electric Field Lines• Electric-field patterns can be visualized with electric

field lines– The way they point indicate direction of E (E is tangent to

electric field lines at each point in space)– Their spacing gives a general idea of the magnitude of E

• General rules for drawing electric field lines:– They begin at positive charges

and end on negative charges– The # of lines drawn leaving

(ending on) a positive (negative) charge is proportional to the magnitude of the charge

– No two field lines can cross each other Electric Field Lines

Electric Field Lines• Two point charges of equal magnitude

but opposite sign form an electric dipole– # lines that begin at positive charge =

# that terminate at negative charge– Very near each charge, lines are nearly

radial– Strong field between the charges– Electric field generated by Gymnarchus

niloticus resembles that of a dipole (electrolocation used to spot prey or predators)

• Electric field lines near 2 equal positive point charges– Why is field weak between the charges?

Interactive Example Problem:Field Lines and Trajectories

Animation and solution details given in class.

(PHYSLET Physics Exploration 23.2, copyright Pearson Prentice Hall, 2004)

Conductors in Electrostatic Equilibrium• An isolated conductor in electrostatic equilibrium (no

net flow of charge) has the following properties:– Electric field is zero everywhere inside “meat” of conductor– Only points on its surface(s) can have a net charge (helpful

while in a car during a thunderstorm)– Electric field at the surface is

perpendicular to the surface– Excess charge is more concentrated

at regions of greater curvature, like sharp points (principle behind use of lightning rods and electrostatic precipitators)

• Michael Faraday’s famous “ice-pail” experiment proved that net charge on conductor in electrostatic equilibrium resides on its surface

Example Problem #15.35

Solution (details given in class):(a) 0 (b) +5 C inside, –5 C outside(c) 0 inside, –5 C outside(d) 0 inside, –5 C outside

–5 C A –5 C charge is lowered into the center of a hollow conductor as shown. Find the magnitude and sign of the charge on the inside and outside of the hollow conductor when the charge is as shown in Figs. (a), (b), (c), and (d) at right.

Electric Flux• When rainwater falls vertically into a bucket, more

(less) rainwater collects in the bucket when its opening is horizontal (tilted)– Water “flux” into bucket is maximized when water falls

through cross-sectional area perpendicular to water flow

• The number of electric field lines that pass through some area perpendicular to the field direction is proportional to the electric flux E

– If area A is perpendicular to E, E = EA, otherwise we find component of E that is perpendicular to surface defined by A (E cos)

– For a closed surface, flux is positive (negative) if more field lines leave (enter) than enter (leave)

cosEAE

Gauss’s Law• Gauss’s Law relates the electric field on a closed

surface–any closed surface–to the net charge enclosed by the surface (Qenc)– Tells you how much charge you have inside

that “box” without looking inside– You just need to look at the field lines that enter or exit

the box

– 0 = 8.85 10–12 C2 / Nm2 (“permittivity of free space”)

• Gaussian surfaces are used to make electric field calculations easy for symmetrical objects– Type of surface depends

on symmetry of the object

0

enc

Q

E

Example Problem #15.45

Solution (details given in class):

(a) 0

(b) directed radially outward

A point charge q is located at the center of a spherical shell of radius a that has a charge –q uniformly distributed on its surface. Find the electric field

(a)for all points outside the spherical shell and

(b)for a point inside the shell a distance r from the center.

2r

qke

CQ 3: If the distance between a point charge and an infinitely large charged plate is increased by a factor of 2, the new force on the point charge will:

A) decrease by a factor of 4. B) decrease by a factor of 2.C) remain the same.D) increase by a factor of 2.