unit three electricity and magnetism no area of physics has had a greater impact on the way we live...

UNIT THREEUNIT THREEElectricity Electricity and and MagnetismMagnetism

No area of physics has

had a greater impact on the

way we live than the study

of electricity and

magnetism.

Chapter 12Chapter 12Electrostatic Electrostatic PhenomenaPhenomena

Lecture PowerPoint

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What does

lightning have in

common...

... with hair on a dry

winter day?

Effects of Electric Charge

Hair seems to have a mind of its own when combed on a dry winter day.

What causes the hairs to repel one another?

Why does a piece of plastic refuse to leave your hand after you peeled it off a package?Why do you get a slight shock after walking across carpet and touching a light switch?

All these phenomena involve different materials rubbing against one another. Electrostatic effects can be demonstrated by rubbing plastic or glass

rods with different furs or fabrics. Small wads of dry, paperlike material called pith balls are light

enough to be strongly influenced by electrostatic forces. When a plastic rod, vigorously rubbed with cat fur, is brought near

the pith balls, at first the pith balls are attracted to the rod like bits of iron to a magnet.

After contacting the rod, the pith balls dance away from the rod.

They are now repelled by the rod and also by each other.

A repulsive force must be acting between the two pith balls after they have been in contact with the rod. Perhaps the balls have received something (call it electric charge)

from the rod that is responsible for the force we observe. This charge was somehow generated by rubbing the rod with the cat

fur. The force that is exerted by one stationary charge on another is

called the electrostatic force.

Experiments with different materials indicate that there are two types of charge.

An electroscope consists of two metallic-foil leaves suspended from a metal post inside a glass-walled container. If the foil leaves are uncharged, they will hang straight down. If a charged rod is brought in contact with the metal ball on top, the

leaves immediately spread apart and stay apart, even if the rod is removed.

If an object of the same charge as the original rod is later brought near the metal ball, the leaves will spread farther apart.

An object with the opposite charge will make the leaves come closer together.

A larger charge produces a larger effect.

Like charges repel each other, and unlike charges attract

each other.


each other.

Benjamin Franklin introduced the names positive and negative for the two types of charge.

He also proposed that a single fluid was being transferred from one object to another during charging. A positive charge resulted from

a surplus of the fluid, and a negative charge resulted from a shortage of the fluid.

Franklin arbitrarily proposedthat the charge on a glass rodwhen rubbed with silk be called positive.


each other.


each other.

Franklin’s model comes surprisingly close to our modern view.

When objects are rubbed together, electrons may be transferred from one object to the other. Electrons are small, negatively

charged particles present in all atoms and, therefore, in all materials.

A negatively charged object has a surplus of electrons, and a positively charged object has a shortage of electrons.

The atomic or chemical properties of materials dictate which way the electrons flow when objects are rubbed together.


each other.


each other.

Conductors and Insulators

Different materials behave differently in the presence of electrostatic forces. Charge can readily flow through conductors:

metals, like copper, silver, iron, gold; our bodies Materials that do not ordinarily permit charge to

flow are insulators: plastic; glass; ceramics; other nonmetallic materials

Charge flows much more readily through several miles of copper wire than through the few inches of insulating ceramic material.

Semiconductors are intermediate between a good conductor and a good insulator.

Their importance to modern technology is enormous.

Can you charge an object without actually touching it with another

charged object? Charging by induction

involves the conducting property of metals: Charge a plastic rod with

cat fur and bring the rod near a metal ball mounted on an insulating post.

The electrons in the metal ball are repelled by the negative rod.

There is a negative charge buildup on the side opposite the rod, and a positive charge on the near side.

Can you charge an object without actually touching it with another

charged object? To charge the ball by

induction, now touch the ball with your finger on the side opposite the rod. The negative charge flows

from the ball to your body, since it is still repelled by the negative rod.

If you now remove your finger and then the rod, a net positive charge is left on the ball.

Charging by induction illustrates the mobility of charges on a conducting object such as the metal ball. The process will not work with a glass ball. Charging by induction is an important process in

machines used for generating electrostatic charges, and in many other practical devices.

It also explains some of the phenomena associated with lightning storms.

Why are insulators attracted to charged objects?

Recall that the pith balls were attracted to the charged rod before they were charged themselves. Electrons are not free to move

in the insulating material of the pith balls.

However, within each atom or molecule, charges can move.

Each atom becomes an electric dipole: the center of the negative charge is slightly displaced from the center of the positive charge.

The material is polarized.

Since the negatively charged surface is closer to the rod than the positively charged surface, it experiences a stronger electrostatic force. The overall effect is that the pith ball is attracted to the

charged rod, even though the net (total) charge on the pith ball is zero.

After the ball comes in contact with the charged rod, some of the charge on the rod is transferred to the pith ball.

The pith ball is then positively charged like the rod, and so is repelled by the rod.

Polarization explains why small bits of paper or styrofoam are attracted to a charged object such as a sweater rubbed against some other material.

Electrostatic precipitators used to remove particles from smoke in industrial smoke stacks use this property. Polarized particles are attracted to charged plates in the

precipitator, removing them from the emitted gases.

The Electrostatic Force: Coulomb’s Law

Coulomb measured how the electrostatic force varies with distance and quantity of charge. Since the electrostatic force is

so weak, he had to develop special techniques, involving a torsion balance.

The degree of twist of the wire measures the repulsive force between the two charges.

Determining the amount of charge on the balls was more difficult.

Although he could not measure absolute quantities of charge on the balls, Coulomb was able to measure the effects due to different relative amounts of charge. By bringing two identical metal balls into contact, one

charged and the other initially uncharged, Coulomb knew he had equal amounts of charge on both balls.

By repeating the process, he could get a ball with exactly half that charge, or one-fourth, etc.

He could then measure how the strength of the electrostatic force varied when the amount of charge was doubled, quadrupled, etc., in addition to how the force varied with distance between the balls.

Coulomb’s Law The electrostatic force between two charged

objects is proportional to the quantity of each of the charges and inversely proportional to the square of each distance between the charges.

229

221

C/mN 109constant sCoulomb'

(C) coulombs of unitsin q

k

r

qkqF

Two positive charges, one 2 C and the other 7 C, are separated by a

distance of 20 cm. What is the magnitude of the electrostatic force that each charge exerts upon the

other? a) 0.32 Nb) 0.63 Nc) 0.70 Nd) 2.02 Ne) 3.15 N

q1 2 C q2 7 C r 20 cm 0.2 m

F kq1q2

r2

9 109 N m2 /C2 2 10 6 C 7 10 6 C

0.2 m 2

0.126 N m2

0.04 m23.15 N

e) .

The electrostatic force has the same inverse-square dependence on distance as Newton’s law of gravitation.

If we double the distance between the charges, the force falls to one-fourth of the original.

The gravitational force depends on the masses, and the electrostatic force depends on the charges.

Gravity is always attractive; there is no such thing as negative mass. Gravity is much weaker than the electrostatic force. Physicists are still trying to understand the reasons for the relative

strengths of the fundamental forces. The search for a unified field theory that would explain the

relationships between all of the fundamental forces is a major area of research in modern theoretical physics.

Fg Gm1m2

r2 and Fe kq1q2

r2

Three positive charges are located along a line as shown. What is the magnitude of the force exerted on the 0.02-C charge by the 0.10-C

charge?

a) 2.25 x 106 Nb) 4.5 x 106 Nc) 9.0 x 106 Nd) 1.8 x 107 Ne) 2.7 x 108 N

q1 0.02 C q2 0.10 C r 2 m

F kq1q2

r2

9 109 Nm2 /C2 0.02 C 0.10 C

2 m 2

4.5 106 N (to the right)

b) .

Three positive charges are located along a line as shown. What is the magnitude of the force exerted on the 0.02-C charge by the 0.04-C

charge?


q1 0.02 C q2 0.04 C r 1 m

F kq1q2

r2

9 109 N m2 /C2 0.02 C 0.04 C

1 m 2

7.2 106 N (to the left)

c) .

Three positive charges are located along a line as shown. What is the net force exerted on the

0.02-C charge by the other two charges?


F F1 F2

7.2 106 N 4.5 106 N

2.7 106 N (to the left)

e) .

The Electric Field

How do the charges exert forces on each other, when they are not even touching? The concept of an electric field describes how

one charge affects the space around it, which then exerts a force on another charge.

The electric field at a given point in space is the electric force per unit positive charge that would be exerted on a charge if it were placed at that point.

It is a vector having the same direction as the force on a positive charge placed at that point.

E F

q

Two point charges, 3 C (left) and 2 C (right), are separated by a distance of 30 cm. A third charge q0 =4 C is placed between them as shown. The force exerted by q1 on q0 is 10.8 N, and the force exerted by q2 on q0 is 1.8 N.What is the net electrostatic force acting on

q0?a) 1.8 N to the leftb) 9 N to the rightc) 10.8 N to the rightd) 12.6 N to the righte) 12.6 N to the left

F F1 F2

10.8 N 1.8 N

9 N (to the right)

b) .

What is the electric field at the location of the charge q0 due to the other two charges?

a) 2.25 x 106 N/C leftb) 3.0 x 106 N/C leftc) 4.5 x 106 N/C leftd) 2.25 x 106 N/C righte) 3.0 x 106 N/C right

E F

q0

9 N

4 10-6 C

2.25 106 N/C (to the right)

d) .

We can then use the field to find the force on any other charge placed at that point:

If the charge q is negative, the minus sign indicates that the direction of the force on a negative charge is opposite to the direction of the field.

The direction of the electric field is the direction of the force exerted on a positive test charge.

We can talk about the field at a point in space even if there is no charge at that point.

The electric field can exist even in a vacuum. The field concept can also be used to define a gravitational

field or a magnetic field, as well as others.

Although Maxwell was the major contributor to the electric field concept, Faraday also developed the idea of field lines as a means of visualizing both the direction and strength of the field.

The direction of the electric field lines around a positive charge can be found by imagining a positive test charge q0 placed at various points around the source charge.The field has the same direction as the force on a positive test charge.


The electric field lines associated with a positive charge are directed radially outward.


A positive test charge is attracted to a negative charge.The electric field lines associated with a negative charge are directed inward, as indicated by the force on a positive test charge, q0.

An electric dipole is two charges of equal magnitude but opposite sign, separated by a small distance.Electric field lines originate on positive

charges and end on negative charges.

The field lines point away from the positive charge, and in toward the negative charge.Near each charge, the electric field approximates the field due to a single point charge of the same sign.

Two charges, of equal magnitude but opposite sign, lie along a line as shown. What are the

directions of the electric field at points A, B, C, and D?

a) A:left, B:left, C:right, D:rightb) A:left, B:right, C:right, D:rightc) A:left, B:right, C:right, D:leftd) A:right, B:left, C:left, D:righte) A:right, B:left, C:right, D:right

c) .

Electric Potential

The electrostatic force is a conservative force, which means we can define an electrostatic potential energy. We can therefore define electric potential or

voltage.

Two parallel metal plates containing equal but opposite charges produce a uniform electric field between the plates.This arrangement is an example of a capacitor, a device to store charge.

A positive test charge placed in the uniform electric field will experience an electrostatic force in the direction of the electric field.

An external force F, equal in magnitude to the electrostatic force qE, will move the charge q a distance d in the uniform field.

The external force does work on the charge and increases the potential energy of the charge.The work done by the external force is qEd, the force times the distance.This is equal to the increase in potential energy of the charge: PE = qEd.This is analogous to what happens when a mass m is lifted against the gravitational force.

Electric potential is related to electrostatic potential energy in much the same way as electric field is related to electrostatic force.

The change in electric potential is equal to the change in electrostatic potential energy per unit of positive test charge:

Electric potential and potential energy are closely related, but they are NOT the same. If the charge q is negative, its potential energy will decrease

when it is moved in the direction of increasing electric potential.

It is the change in potential energy that is meaningful.

V PE

q in units of volts (V)

1 J/C 1 V

PE qV

Two plates are oppositely charged so that they have a uniform electric field of 1000 N/C between

them, as shown. A particle with a charge of +0.005 C is moved from the bottom (negative)

plate to the top plate. What is the change in potential energy of the charge?

a) 0.15 Jb) 0.3 Jc) 0.5 Jd) 0.8 Je) 1.5 J

a) .

PE W Fd qEd

(0.005 C)(1000 N/C)(0.03m)

0.15 J

What is the change in electric potential from the bottom to the top plate?

a) 0.15 Vb) 0.3 Vc) 5 Vd) 30 Ve) 150 V

V PE

q

0.15 J

0.005 C30 V

d) .

The potential energy of a positive charge increases when we move it against the field. For a uniform electric field, there is a simple

relationship between the magnitude of the electric field and the change in electric potential: V = Ed.

For non-uniform fields, the relationship is more complicated, but the electric potential always increases most rapidly in the direction opposite to the electric field.For a positive point charge, the electric potential increases as we move closer to the charge.

What is lightning?What is lightning? Most thunderclouds generate a separation of Most thunderclouds generate a separation of

charge resulting in a net positive charge near the charge resulting in a net positive charge near the top and a net negative charge near the bottom.top and a net negative charge near the bottom.

The charge separation produces strong electric The charge separation produces strong electric fields in the cloud as well as between the cloud and fields in the cloud as well as between the cloud and earth.earth.

Since moist earth is a reasonably good conductor, a Since moist earth is a reasonably good conductor, a positive charge is induced on the surface of the positive charge is induced on the surface of the earth below the cloud.earth below the cloud.

Most thunderclouds generate a separation of Most thunderclouds generate a separation of charge resulting in a net positive charge near the charge resulting in a net positive charge near the top and a net negative charge near the bottom.top and a net negative charge near the bottom.

The charge separation produces strong electric The charge separation produces strong electric fields in the cloud as well as between the cloud and fields in the cloud as well as between the cloud and earth.earth.

Since moist earth is a reasonably good conductor, a Since moist earth is a reasonably good conductor, a positive charge is induced on the surface of the positive charge is induced on the surface of the earth below the cloud.earth below the cloud.

The electric field generated can be several thousand volts per meter; the potential difference between the cloud’s base and the earth can easily be several million volts!

This creates an initial flow of charge (the “leader”) along a path that offers the best conducting properties over the shortest distance.

The leader ionizes some of the atoms in the air along that path.The following strokes all take place along this same path in rapid succession.The heating and ionizing produce the lightning we see.The thunder (sound waves) is produced at the same time, but takes longer to reach us since sound travels slower than light.