Chapter 15 Electric Charge

Main Points of Chapter 15

- Charge
- Electric forces
- Two types of charge
- Induction
- Conservation and quantization of charge
- Coulombs law
- Forces involving multiple charges

15-1 Chargea Property of Matter

- A Brief History of the Study of Electricity
- and Magnetism

2. The Significance of Electric Forces

The Electric Force is responsible for

- electrons binding to a positive nucleus,
- forming a stable atom

- atoms binding together into molecules

- atoms or molecules binding together into
- liquids and solids

- forces such as friction and other contact forces

3. Matter and Electric Charge

1) The Origin of Charge

The atom is electrically neutral

number of e number of p

Charge is an intrinsic property of matter

2) Conductors and Insulators

Materials in which the outermost electron(s) that

are very loosely bound to the atoms, and can move

freely through the material are called

conductors.

- metal

Materials in which charge does not move easily

are called insulators.

- glass, plastics, paper

A Electrons are free to move in a conductor.

A Electrons stay with their atom in an insulator.

3) Charging by friction

We can transfer charge from one material to

another suitable material simply by rubbing

Electric charges are of two types, called

positive () and negative (-)

Like charges repel, and unlike charges attract.

We know that when glass is rubbed with silk,

electrons are transferred from the glass to the

silk. Because the silk is negatively charged,

electrons are said to carry a negative charge

Electrons have a negative charge because of a

historical choice rather than because of an

intrinsic physical property.

In the presence of a charged object, a neutral

object can polarize the charges opposite to

those on the charged object move closer to it,

and the other charges move away.

4) Charging by Induction

Charge is measured in Coulombs (C)

The smallest unit of charge is the magnitude of

the charge on the electron

- ACT Two neutral conductors are connected by a

wire and a charged rod is brought near, but does

not touch. The wire is taken away, and then the

charged rod is removed. What are the charges on

the conductors?

Follow-up What will happen when the conductors

are reconnected with a wire?

4. The Electroscope

The electroscope is a device that detects the

presence of excess free charge on an object. This

can be done in two ways

First, when a charged rod transfers charge

directly to the electroscope, that charge spreads

uniformly over its metal surfaces. The leaf and

stem then have same-sign charges, and repel.

Second, when a charged rod is brought near, but

not touching, the electroscope, it attracts

opposite charges. The like charges tend to move

away from the rod once again the stem and leaf

have same-sign charges, and repel.

15-2 Charge is Conserved and Quantized

1.Charge is conserved

Charge by friction

Charge by Induction

In observed reactions involving the so-called

elementary particles, no one has ever seen a

single case of net charge appearing or

disappearing.

Radioactive decay of nuclei

The algebraic sum of all the electric charges in

any closed system is constant.

Principle of conservation of charge

2.Charge is quantized

Free charge is quantized in positive or negative

integral multiples of e

15-3 Coulombs Law

1. Point charge (charged particle)

a point-like object with none zero electric charge

Coulombs torsion balance

2. Coulombs law

- The electric force between charges q1 and q2 is
- attractive if charges have opposite signs
- repulsive if charges have same signs

The magnitude F of the electric force between two

point charges is directly proportional to the

product of the charges and inversely proportional

to the square of the distance between them.

Where k is a proportionality constant whose

numerical value depends on the units used for

charge.

the permittivity of free space

3. Define the Columb

- Act How many electrons are there in one coulomb
- of negative charge?

Solution

The number of electrons is equal to the charge q

divided by the charge e on each electron.

The number N of electrons is

This number is enormous.

There is as much as 25 coulombs can be

transferred between the cloud and the ground in

a lightning bolt. The typical charges produced

in the laboratory are much smaller and are

measured conveniently in microcoulombs.

4. Discussion

- Coulombs law describes only the interaction
- of two point charges

b. The two forces obey Newtons third law

c. Electric force vs. gravitational force.

- Example The nucleus in an iron atom has a radius

of about 4.0 10-15 m and contains 26 protons. - (a) What is the magnitude of the repulsive

electrostatic force between two of the protons

that are separated by 4.0 10-15 m?

(b) What is the magnitude of the gravitational

force between those same two protons?

Solution

The gravitational force is negligible in

comparison to the electrostatic force.

The protons are bound together by an enormous

force called the strong nuclear force.

15-4 Forces Involving Multiple Charges

1. Principle of Superposition

When there are multiple charges, the net

force on any one of them is the vector sum of the

forces due to each of the others.

- ACT A circular ring of charge of radius a and

total charge Q lies in the x-y plane with it

center at the origin. The direction of the force

on a very small segment of this ring is directed

________ if Q is negative. - A) along the negative z-axis
- B) in no direction since the force is zero
- C) outward from the origin
- D) inward toward the origin
- E) along the positive z-axis

- ACT Three equal charges are located at the

corners of an equilateral triangle. If the length

of the sides of the triangle are doubled and each

of the charges is doubled, then the resulting

force on each of the charges ________ - A) doubles.
- B) quadruples.
- C) is halved.
- D) stays the same.
- E) changes by a factor of 1.414.

2. Continuous Distributions of Charges

For a continuous distribution of charge, first

think of it as a collection of very small charges

The total force is found by summing the force

from each piece

If we know the charge density as a function of

position, we can go to the limit where the

charges are infinitesimally small, and integrate.

Q

l the linear charge density

s the surface charge density

r the volume charge density

In practice, such integrals involve three

one-dimensional integrals.

- Example Figure below shows two particles fixed

in place a particle of charge q1 8q at the

origin and a particle of charge q2 -2q at x

L. At what point (other than infinitely far away)

can a proton be placed so that it is in

equilibrium (meaning that the net force on it is

zero)? Is that equilibrium stable or unstable?

Solution

If the proton at point R

The equilibrium at x2L is unstable

- Example A point charge Q is located at a

distance a from one end of a charged object with

electric line density ? and length L, as shown in

the following figure. Find the force on the

charge Q.

Solution

Q

a

O

x

L

left

If Lltlt a , F ?

point charge result

- Example A charge is spread uniformly along the
- y-axis from y0 to The charge

density on - the y-axis is l Find the force on a point

charge q - placed on the x-axis at xx0

y

Solution

q

x

x0

- Example Find the force on a point charge q1

located - on the axis of a uniformly charged ring of total

charge q - The radius of the ring is R, and q1 is located a

distance x - from the center of the ring.

Solution

R

q1

x

x

If x0,

If xgtgtR

- Example Calculate the force exerted on a charge

q1 by - an infinite plane sheet with surface charge

density - (charge per unit area) s.

s

Solution

q1

Break up the plane into concentric rings.

x

x

Use the results of last example

(No Transcript)

3. The Force Due to a Spherical Symmetric

Charge Distribution

The two shell theorems

A shell of uniform charge attracts or repels a

charged particle that is outside the shell as if

all the shell's charge were concentrated at its

center.

If a charged particle is located inside a shell

of uniform charge, there is no net electrostatic

force on the particle from the shell.

If a charge distribution is spherically symmetric

Summary of Chapter 15

- Electric charge comes in two types, positive and

negative. - Opposite charges attract like charges repel.
- Metals are good conductors electrons are able

to move freely through them most other materials

are insulators - Basic charge is that on the electron

- All other charges are multiples of e.

Summary of Chapter 15, cont.

- Charge is conserved net charge before an

interaction is the same as net charge afterwards - Coulombs law for the force between two point

charges

- For multiple, or continuous, charges, the

superposition principle applies.