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Chapter 33 Electric Fields and Potential

33.1 Electric Fields • The space around every electric charged is

filled with an electric field.

• An electric field has both magnitude and direction.

• The magnitude describes the electric field’s strength.

• The direction of an electric field is always from positive to negative.

33.2 Electric Field Lines • A useful way to describe an electric field in

place of vectors is with electric field lines, also called lines of force.

• Where the lines are farther apart, the field is weaker.

Vector Nature of Electric Forces

• Two point charges are separated by a distance r

• The like charges produce a repulsive force between them

• The force on q1 is equal in magnitude and opposite in direction to the force on q2

Vector Nature of Forces

• Two point charges are separated by a distance r

• The unlike charges produce a attractive force between them

• The force on q1 is equal in magnitude and opposite in direction to the force on q2

Electrical Forces are Field Forces

• This is the second example of a field force

Recall that Gravity was the first ex.

• Remember, with a field force, the force is exerted by one object on another object even though there is no physical contact between them.

• There are some important differences between electrical and gravitational forces.

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Electrical Force Compared to Gravitational Force

• Both are inverse square laws.

• The mathematical form of both laws is the same.

• Electrical forces can be either attractive or repulsive.

• Gravitational forces are always attractive.

QUICK QUIZ 32.2

Object A has a charge of +2 µC, and

object B has a charge of +6 µC.

Which statement is true:

(a) FAB = –3FBA, (b) FAB = –FBA, or

(c) 3FAB = –FBA

QUICK QUIZ 32.2 ANSWER

(b). By Newton’s third law, the two

objects will exert forces having equal

magnitudes but opposite directions on

each other.

The Superposition Principle

• The resultant force on any one charge equals the vector sum of the forces exerted by the other individual charges that are present.

– Remember to add the forces vectorially

Superposition Principle Example

• The force exerted by q1 on q3 is F13

• The force exerted by q2 on q3 is F23

• The total force exerted on q3 is the vector sum of F13 and F23

Electrical Field

• Maxwell developed an approach to discussing fields

• An electric field is said to exist in the region of space around a charged object

– When another charged object enters this electric field, the field exerts a force on the second charged object

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Electric Field, cont.

• A charged particle, with charge Q, produces an electric field in the region of space around it

• A small test charge, qo, placed in the field, will experience a force

Electric Field

• Mathematically, E = F/qo

• Use this for the magnitude of the field

• The electric field is a vector quantity

• The direction of the field is defined to be the direction of the electric force that would be exerted on a small positive test charge placed at that point

Direction of Electric Field

• The electric field produced by a negative charge is directed toward the charge

– A positive test charge would be attracted to the negative source charge

Direction of Electric Field, cont

• The electric field produced by a positive charge is directed away from the charge – A positive test charge

would be repelled from the positive source charge

QUICK QUIZ 32.4

A Styrofoam ball covered with a conducting

paint has a mass of 5.0 10-3 kg and has a

charge of 4.0 C. What electric field

directed upward will produce an electric

force on the ball that will balance the weight

of the ball?

(a) 8.2 102 N/C (b) 1.2 104 N/C (c)

2.0 10-2 N/C (d) 5.1 106 N/C

QUICK QUIZ 32.4 ANSWER

(b). The magnitude of the upward

electrical force must equal the weight of

the ball. That is: qE = mg, so

4.0 10-6 C (E) = 5.0 10-3 kg (9.8 m/ss) E = 5.0 10-3 kg (9.8 m/ss)/4.0 10-6 C

= 1.2 x 104 N/C

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QUICK QUIZ 32.5

A circular ring of radius b has a total

charge q uniformly distributed around

it. The magnitude of the electric field

at the center of the ring is

(a) 0 (b) keq/b2 (c) keq2/b2

(d) keq2/b (e) none of these.

QUICK QUIZ 32.5 ANSWER

(a). If a test charge is at the center of

the ring, the force exerted on the

test charge by charge on any small

segment of the ring will be balanced

by the force exerted by charge on

the diametrically opposite segment

of the ring. The net force on the test

charge, and hence the electric field

at this location, must then be zero.

Electric Field Line Patterns

• Point charge

• The lines radiate equally in all directions

• For a positive source charge, the lines will radiate outward

Electric Field Line Patterns

• For a negative source charge, the lines will point inward

Electric Field Line Patterns

• An electric dipole consists of two equal and opposite charges

• The high density of lines between the charges indicates the strong electric field in this region

Electric Field Line Patterns

• Two equal but like point charges

• At a great distance from the charges, the field would be approximately that of a single charge of 2q

• The bulging out of the field lines

between the charges indicates the repulsion between the charges

• The low field lines between the charges indicates a weak field in this region

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Electric Field Patterns

• Unequal and unlike charges

• Note that two lines leave the +2q charge for each line that terminates on -q

Rules for Drawing Electric Field Lines

• The lines for a group of charges must begin on positive charges and end on negative charges

– In the case of an excess of charge, some lines will begin or end infinitely far away

• The number of lines drawn leaving a positive charge or ending on a negative charge is proportional to the magnitude of the charge

• No two field lines can cross each other

QUICK QUIZ 32.7

Rank the magnitudes of the electric field at points A, B,

and C in the figure below, largest magnitude first.

QUICK QUIZ 32.7 ANSWER

A, B, and C. The field is greatest at point

A because this is where the field lines

are closest together. The absence of

lines at point C indicates that the electric

field there is zero.

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Conductors in Electrostatic Equilibrium

• When no net motion of charge occurs within a conductor, the conductor is said to be in electrostatic equilibrium

• An isolated conductor has the following properties: – The electric field is zero everywhere inside the conducting material

– Any excess charge on an isolated conductor resides entirely on its surface

– The electric field just outside a charged conductor is perpendicular to the conductor’s surface

– On an irregularly shaped conductor, the charge accumulates at locations where the radius of curvature of the surface is smallest (that is, at sharp points)

Property 1

• The electric field is zero everywhere inside the conducting material

– Consider if this were not true

• if there were an electric field inside the conductor, the free charge there would move and there would be a flow of charge

• If there were a movement of charge, the conductor would not be in equilibrium

33.3 Electric Shielding • What happens when a car is struck by lightning?

• An example of electric shielding is a car being struck by lightning.

• When a car is struck by lightning, the occupants in the car are safe. This is because the electrons that strike the car are mutually repelled and spread over the metal surface, then discharge into the ground.

• The electric field inside the car is practically zero.

• Can we shield from Gravity?

• http://www.youtube.com/watch?v=Zi4kXgDBFhw

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Property 2

• Any excess charge on an isolated conductor resides entirely on its surface

– A direct result of the 1/r2 repulsion between like charges in Coulomb’s Law

– If some excess of charge could be placed inside the conductor, the repulsive forces would push them as far apart as possible, causing them to migrate to the surface

Property 3

• The electric field just outside a charged conductor is perpendicular to the conductor’s surface – Consider what would happen

it this was not true

– The component along the surface would cause the charge to move

– It would not be in equilibrium

Property 4

• On an irregularly shaped conductor, the charge accumulates at locations where the radius of curvature of the surface is smallest (that is, at sharp points)

More on Property 4

• Any excess charge moves to its surface

• The charges move apart until an equilibrium is achieved

• The amount of charge per unit area is greater at the flat end

• The forces from the charges at the sharp end produce a larger resultant force away from the surface

• Why a lightning rod works

Electric Flux

• Field lines penetrating an area A perpendicular to the field

• The product of EA is the flux,

• In general:

E = E A cos

More on Electric Flux

E = E A cos

– The perpendicular to the area A is at an angle to the field.

– When the area is constructed such that a closed surface is formed, use the convention that flux lines passing into the interior of the volume are negative and those passing out of the interior of the volume are positive.

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33.4 Electrical Potential Energy • A charged object has potential energy by virtue

of it location in an electric field. This is called electric potential energy.

• The small positive charge has more potential energy when it is closer to the positively charged sphere because work is required to move it closer.

Gravitational Potential Energy

Electrical

Potential Energy

Depends on location

-- distance from source of gravity (ground)

Depends on location

-- distance from source of electric field

Get more PE by doing work

Get more PE by doing work

33.5 Electric Potential

• Electrical potential is the amount of electrical potential energy per charge.

• The equation for electric potential: electric potential = electrical potential energy

____________________________

charge

• The SI unit for electric potential is volt.

• Electric potential is commonly called voltage.

• Typical voltage sources include:

dry cell (battery)

generator

car battery

Work and Potential Energy

• There is a uniform field between the two plates

• As the charge moves from A to B, work is done in it

• W = F d= q E d

• ΔPE = - W = - q E d

– only for a uniform field

Work and Potential Energy

• There is a uniform field between the two plates

• As the charge moves from A to B, work is done in it

• W = F d= q E d

• ∆PE = -WAB = - qEd

Note: This is only for a uniform field

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Energy and Charge Movements

• A positive charge gains electrical potential energy when it is moved in a direction opposite the electric field

• If a charge is released in the electric field, it experiences a force and accelerates, gaining kinetic energy – As it gains kinetic energy, it loses an equal amount of

electrical potential energy

• A negative charge loses electrical potential energy when it moves in the direction opposite the electric field

Energy and Charge Movements, cont

• When the electric field is directed downward, point B is at a lower potential than point A

• A positive test charge that moves from A to B loses electric potential energy

• It will gain the same amount of kinetic energy as it loses potential energy

Summary of Positive Charge Movements and Energy

• When a positive charge is placed in an electric field

– It moves in the direction of the field

– It moves from a point of higher potential to a point of lower potential

– Its electrical potential energy decreases

– Its kinetic energy increases

Summary of Negative Charge Movements and Energy

• When a negative charge is placed in an electric field

– It moves opposite to the direction of the field

– It moves from a point of lower potential to a point of higher potential

– Its electrical potential energy decreases

– Its kinetic energy increases

Application – Electrostatic Precipitator

• It is used to remove particulate matter from combustion gases

• Reduces air pollution

• Can eliminate approximately 90% by mass of the ash and dust from smoke

Application – Electrostatic Air Cleaner

• Used in homes to relieve the discomfort of allergy sufferers

• It uses many of the same principles as the electrostatic precipitator

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Application – Xerographic Copiers

• The process of xerography is used for making photocopies

• Uses photoconductive materials

– A photoconductive material is a poor conductor of electricity in the dark but becomes a good electric conductor when exposed to light

The Xerographic Process

Application – Laser Printer

• The steps for producing a document on a laser printer is similar to the steps in the xerographic process – Steps a, c, and d are the same

– The major difference is the way the image forms of the selenium-coated drum

• A rotating mirror inside the printer causes the beam of the laser to sweep across the selenium-coated drum

• The electrical signals form the desired letter in positive charges on the selenium-coated drum

• Toner is applied and the process continues as in the xerographic process

VI. Electrical Energy Storage

• A. Capacitor

– A device used to store energy in a circuit

• B. Simplest capacitor is a pair of conducting plates separated by a small distance

• pictures of capacitors – Connect to a charging device (like a battery)

– Charge transferred from one plate to other

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• C. Discharged when a conducting path is provided between them

• D. Energy stored in a capacitor = the energy stored in an electric field

Capacitance

• A capacitor is a device used in a variety of electric circuits

• The capacitance, C, of a capacitor is defined as the ratio of the magnitude of the charge on either conductor (plate) to the magnitude of the potential difference between the conductors (plates)

Capacitance, cont

• C = Q/∆V

• Units: Farad (F)

– 1 F = 1 C / V

– A Farad is very large!

• You often will see µF or pF

Parallel-Plate Capacitor

• The capacitance of a device depends on the geometric arrangement of the conductors

• For a parallel-plate capacitor whose plates are separated by air:

C = EoA/d

Where d is the distance between plates, A is the area, and Eo is the permattivity of free space.

Applications of Capacitors – Camera Flash

• The flash attachment on a camera uses a capacitor

– A battery is used to charge the capacitor

– The energy stored in the capacitor is released when the button is pushed to take a picture

– The charge is delivered very quickly, illuminating the subject when more light is needed

Applications of Capacitors -- Computers

• Computers use capacitors in many ways – Some keyboards use

capacitors at the bases of

the keys

– When the key is pressed, the capacitor spacing decreases and the capacitance increases

– The key is recognized by

the change in capacitance

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Applications

• Defibrillators – When fibrillation occurs, the heart produces a

rapid, irregular pattern of beats

– A fast discharge of electrical energy through the heart can return the organ to its normal beat pattern

• In general, capacitors act as energy reservoirs that can slowly charged and then discharged quickly to provide large amounts of energy in a short pulse

33.6 Electric Energy Storage

• A capacitor is a device that can store electrical energy.

• The energy stored in a capacitor is energy stored in electric fields.

This is an

early

VandeGraaff

generator

Demonstrated

by Robert J.

Van de Graaff

Safety First! • VandeGraaff: high voltage

(10,000V), low current (electron flow)

• Wall: low voltage (120V), high current (lots electrons)

• Heart devices – caution!

History • Dr. Robert J. Van de Graaff

designed and built the generator in the early 1900’s. He was a professor at MIT. This generator was originally used as a research tool in early atom-smashing and high energy X-ray experiments.

33.7 The Van de Graff Generator

• A motor driven rubber belt is supplied electrons. The electrons are deposited on the metal dome.

• Due to mutual repulsion, the electrons move to the

outside of the metal dome, leaving room for more electrons to build up.

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Quick Quiz

• What is the magnitude of the force acting on an alpha particle that is placed in an electric field of 400 N/C?

Demos • Streamers

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• Bubbles

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• Fluorescent current - Freaky!

• Hair raising experience!