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Chapter 22Electrostatics II

Electric Field & Potential

Lecture 24

Chapter 23Electric Current

From last time--• Electric charge (q), measured in Coulombs (C)• Positive and negative charge• Electric force; like charges repel, unlike charges attract• Coulomb’s Law: Force between charges q1 & q2 a

distance d apart, where k is the “electric constant” with value 9.0 x 109 Nm2/C2

221

dqqkF =

Electric Field (E)Electric field• Electric disturbance in space surrounding an electric

charge (an energetic aura)• Size of the electric field at a point in space is the electric

force that would act on a 1C charge placed there (force per unit charge).

• Vector quantity; direction is the direction of the electric force that would act on a positive “test charge”

E = F/qA “field point”

Direction of Electric Field at field point

Source charge

Electric FieldElectric field direction• Same direction as the electric force that would

act on a positive charge placed in the field• Opposite direction to the electric force that would

act on an electron placed in the field

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Electric Field LinesElectric field lines trace out the direction of electric force that would act if a positive “test”charge were placed in the electric field at points in space.

E Field in Conductors• Material in which some electrons move freely• Most good conductors are metals• “Free” electrons in conductor move until E = 0

everywhere within the material of the conductor

+

++

+

+

Conducting sphereFree electrons movetoward external + chg.

Pos. charge (protons)left behind

+

• Field from surface charge cancels field from external charge everywhere in the conductor. E = 0 everywhere inside.

• No charge found in body of conductor --all charge on surface (whether or not there is net charge)

• Note that external charge can exert a force on a neutral conductor via polarization (last lecture)

Hollow Conductors• E=0 in the empty space of a hollow conductor

(unless free charge is placed in the space)

• We say the interior space is shielded from electric fields. This can work even if there are holes in shield:

• Demo

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Electric Potential EnergyPotential energy associated with electric force, similar to potential energy associated with gravitational force.

GravityForce Electric

Force

Electric Potential Energy• Remember gravitational potential energy

U = mgh for object of mass m at height h above zero potential reference position (valid near Earth surface)– Describes energy stored when work done

against conservative force (gravity)– g is strength of Earth gravitational field (in

N/kg)– We must do work on mass m to increase its

gravitational potential energy (have to lift it to greater height)

• A charged particle in an electric field has electric potential energy

Electric Potential Energy

(a)The spring has more elastic PE when compressed.

(b) The small charge similarly has more PE when pushed closer to the charged sphere. In both cases, the increased PE is the result of work input.

Electric Potential (V)

Electric potential (voltage) at a location:• The Electric Potential Energy per unit charge a

charge would have at that location• May be called voltage• In equation form:

electric potential energyElectric potential =amount of charge

qPEV =

Electric potential (voltage)-- continued• Unit of measurement: volt (V)

Example:• A charge of 20 µC is placed at a location where the

electric potential is 200 V. What is the electric potential energy of the charge?

• The charge is moved to a location where its electric potential energy is 0.002 J. What is the electric potential?

1 volt =1 coulomb1 joule

+

Electric potential (voltage) (continued)

Example:• A charge of 20 µC is placed at a location where the

electric potential is 200 V. What is the electric potential energy of the charge?

V = PE/q so PE = q•V = (20 x 10-6 C)(200V)= 4 X 10-3 J

• The charge is moved to a location where its electric potential energy is 0.002 J. What is the electric potential?

V = PE/q = (0.002J)/(2 x 10-5 C) = 100 V

Electric potential energy is measured in joules. Electric potential, on the other hand (electric potential energy per charge), is measured

A. in volts.B. in watts.C. in amperes.D. also in joules.

Electric PotentialCHECK YOURSELF

Electric potential energy is measured in joules. Electric potential, on the other hand (electric potential energy per charge), is measured

A. in volts.B. in watts.C. in amperes.D. also in joules.

Electric PotentialCHECK YOURSELF

Electric Potential

Electric potential (voltage) (continued)• High voltage can give fairly low electric potential

energy to a very small amount of charge.• High voltage will give high electric potential

energy to an object with lots of charge.

Dangerous?

Voltage Measurement: Voltmeter

A voltmeter measures the electric potential difference (voltage difference, or just “voltage”) between two points. + -

Red Wire

Black Wire

Example

• If it takes 200J of work to move a charge of 2 mC from point D to point C in the picture, what is the voltage between the those two points?

Example• If it takes 200J of work to move a charge

of 2 mC from point D to point C in the picture, what is the voltage between the those two points?

V = PE/q = 200J/(2 x 10-3 C) = 1 x 105 J/C= 1 X 105 V

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Chapter 23Electric Current

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Current

Water continues to flow because a difference in pressure is maintained with the pump.

Water flows from the reservoir of higher pressure to the reservoir of lower pressure; flow stops when the pressure difference ceases.

Flow of Charge• When the ends of an electrical conductor are at

different electric potentials—when there is a potential difference—charge flows from one end to the other.– Analogous to water flowing from higher pressure to

lower pressure

Flow of Charge• To attain a sustained flow of charge in a conductor,

some arrangement must be provided to maintain a difference in potential while charge flows from one end to the other.– A continuous flow is possible if the difference in water

levels—hence the difference in water pressures—is maintained with the use of a pump.

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Electric Current (I)

Just as water current is flow of water molecules, electric current is the flow of electric charge.

In circuits, electrons make up the flow of charge.

ON

OFF

Which of these statements is true?

A. Electric current is a flow of electric charge.B. Electric current is stored in batteries.C. Both A and B are true.D. Neither A nor B are true.

Electric CurrentCHECK YOURSELF

Which of these statements is true?

A. Electric current is a flow of electric charge.B. Electric current is stored in batteries.C. Both A and B are true.D. Neither A nor B are true.

Explanation:Energy, not current, is stored in batteries. The battery uses chemical energy increase the electric potential energy of chargeby “lifting” the charge to a higher voltage. The voltage difference between the ends of the battery will produce a current in a connected circuit.

Electric CurrentCHECK YOURSELF

Electric Current (I)

Rate of electric charge flow• Unit of electric current is the Ampere (A)

1 Ampere = 1 Amp = 1A = 1 coulomb of charge passing a point per second

• Speed of electrons (drift speed) through a wire is slow because of continuous bumping of electrons in wire.

• Charge flows through a circuit; voltage is established across a circuit.

Example

• 3C of charge passes a point in 10s. What is the current?

I = q/(∆t) = 3C/(10 s) = 0.3 A

Direct (Electric) Current -- DCDirect Current• Current always flows in same general direction• Charge moves due to a voltage difference

produced by a battery, DC generator, or solar cell.• Amount of current may vary, but current never

reverses direction.

Alternating Current (AC)Alternating current• Current reverses direction every so often. In US power

system current goes through a set of two reversals 60 times per second (60Hz.)

• Charge moves due to a alternating voltage difference produced by an ac generator (alternator).

• Commercial electric power throughout the world uses ac. As we will see later, “transformers” can step ac from an alternator up to very high voltage for transmission over great distances with small heat losses, then step it back down to lower voltage for safety where energy is consumed.

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AmmeterAmmeter measures electrical current.

Battery

CU

RR

EN

T

Ammeter

Ammeter

Current increases as the voltage increases.

Due to charge conservation, same current into and out of light bulb.

Light Bulb

Ammeter readings always the same.

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Voltage SourcesCharges flow only when they are “pushed” or “driven.” A

sustained current requires a suitable pumping device to provide a difference in electric potential (a voltage).

Simple Chemical Battery Simple Mechanical Generator

Lemon

Copper

Aluminum

Chemical BatteryBatteries separate

positive and negative charges by using a chemical reaction.

Chemical potential energy is converted into electric potential energy.

Rechargeable BatteryEventually the battery’s chemicals are consumed

unless the reaction can be reversed by passing a current into the battery.

Automobile battery is recharged while the gasoline engine is running since the engine powers a generator that produces a recharging current.Starting the car

Engine running

Key Points of Lecture 24Key Points of Lecture 24

Before Monday, read Hewitt Chap. 23 (first half).

Homework #16 due by 11:00 PM Friday Oct. 22.

Homework #17 due by 11:00 PM Tuesday Oct. 26.

• Electric Field• Electric Potential Energy• Electric Potential• Electric Current• DC & AC• Voltage Sources