ElectrostaticsElectrostatics

Lessons from the LabLessons from the Lab

• Opposites attract, likes repel• Charged objects can attract

neutral objects• Attraction is proportional to

charge, distance

• Positive charge results from removing electrons from a substance

• Negative charge results from adding electrons to a substance

• Conducting materials allow charge to flow freely

• Insulating materials do not

Properties of “Charge”Properties of “Charge”

• Reflects relative number of electrons in a substance

• Conserved• Units of Coulombs (C)• An electron has a charge of

1.6 x 10-19C of charge

Significant Charge Significant Charge AmountsAmounts

• When we rub balloons on rabbit hair in the lab, we’re generating 10’s of C

Which of the following will tell Which of the following will tell you you without a doubtwithout a doubt that an that an

object is chargedobject is charged

• 1) It attracts another object that has been rubbed with rabbit fur

• 2) It repels another object that has been rubbed with fur

• 3) It does not attract a neutral object

Three aluminum balls are suspended Three aluminum balls are suspended from the ceiling. All three are charged from the ceiling. All three are charged with various materials. It is found that with various materials. It is found that 1 and 2 repel one another, and 2 and 3 1 and 2 repel one another, and 2 and 3 repel one another. From this, we can repel one another. From this, we can

conclude that:conclude that:

• 1) 1 and 3 carry the same charge• 2) 1 and 3 carry opposite charges• 3) all three carry the same charge• 4) one of the objects carries no

charge• 5) we need more experiments to

determine charge

Three aluminum balls are suspended Three aluminum balls are suspended from the ceiling. Two of the three are from the ceiling. Two of the three are

then charged with various materials. It then charged with various materials. It is found that 1 and 2 attract one is found that 1 and 2 attract one another, and 2 and 3 repel one another, and 2 and 3 repel one

another. From this, we can conclude another. From this, we can conclude that:that:

• 1) 1 and 3 carry the same charge• 2) 1 and 3 carry opposite charges• 3) all three carry the same charge• 4) one of the objects carries no

charge• 5) we need more experiments to

determine charge

Which spheres experience Which spheres experience the greatest attraction?the greatest attraction?

Methods of ChargingMethods of Charging

Charging by FrictionCharging by Friction

• http://phet.colorado.edu/new/simulations/sims.php?sim=John_Travoltage

Charging by InductionCharging by Induction

• http://phet.colorado.edu/new/simulations/sims.php?sim=Balloons_and_Static_Electricity

Charge polarizationCharge polarization

• When the charges in a material arrange themselves in such a way that the material has + and – sides, the material is said to be polarized

Why does Induction Work?Why does Induction Work?

• Both positive and negative charges are still in a substance

• Why is it attracted?

Charging by Charging by Contact/ConductionContact/Conduction

• The physical movement of charge from one object to another

What will happen to two neutral spheres What will happen to two neutral spheres below when you bring a + charged rod close below when you bring a + charged rod close

by?by?

• 1) A and B will become + • 2) A and B will become -• 3) The spheres will remain neutral• 4) A will become – and B will

become +• 5) A will become + and B will

become -

If you want A to remain – and B to If you want A to remain – and B to remain +, what should you do?remain +, what should you do?

• 1) Remove the rod• 2) Separate the spheres and then

remove the rod• 3) Remove the rod, then separate

the spheres• 4) Touch the spheres with the rod

LightningLightning

• We’ve talked about ways to generate attraction and repulsion with charged objects

• Just to review, on what does the attraction depend?

• Assuming you’ve got two charged objects, write a basic equation that describes the force of attraction between them (just worry about the magnitude)

Coulomb's LawCoulomb's Law

• Coulomb’s Law gives us a way to calculate the force between two charged objects

•FE = kq1q2/d2

• k is a constant = 8.99 x 109 N m2/C2

Similarities to GravitySimilarities to Gravity

• Recall how we calculated the gravitational force between objects:

•FG = Gm1m2/d2

• G is a constant = 6.67 x 10-11 N m2/kg2

• Look familiar?

Different ConstantsDifferent Constants

• G = 6.67E-11, k = 8.99e9• What does this tell us about the

difference between gravitational forces and electrostatic forces?

• Calculate the electrostatic force between a +6C charge and a -5C charge, located 2m apart

• Calculate the electrostatic force between a proton in the nucleus of the atom (q = +1.60e-19C) and an electron (q = -1.60e-19C) located in an outer energy level (d = 3e-11m)

• Calculate the electron’s acceleration

LevitationLevitation

• I once heard a person ask, couldn’t you make a person float using charges?

• Perhaps• Imagine a person (m = 70kg)

gathered -10mC of charge by rubbing herself with rabbit fur

• What charge would we need to lift her off the ground?

Examine the configuration Examine the configuration below. Which charge would below. Which charge would exert the greatest force on exert the greatest force on

the -2 charge? the -2 charge?

• 1. +8 2. +4• 3. +6 4. +20

Which list below ranks the Which list below ranks the charges in order of charges in order of

increasing force on the -2 increasing force on the -2 charge?charge?

• 1. A, B, D, C• 2. A, C, B, D• 3. D, C, B, A• 4. C, A, B, D• 5. D, B, C, A

Which arrow represents the direction of the Which arrow represents the direction of the net force on the -2 charge?net force on the -2 charge?

Electric FieldsElectric Fields

• Like gravity, the electrostatic force is a non-contact force

• To conceptually deal with this, we talk about electric fields

• This is a region of space surrounding a charged particle that “carries” the electrostatic force

• An electric field tells us the direction of the electrostatic force

• It also gives us a sense of the force magnitude

Drawing the FieldDrawing the Field

• Place a positive “test” charge near a charge, or charge configuration

• Determine the direction of the net force acting on that positive charge

• Draw an arrow in that direction (arrow length represents force magnitude)

• Move the charge to another place and repeat

A single positive chargeA single positive charge

Which diagram correctly Which diagram correctly illustrates the field illustrates the field

surrounding a negative point surrounding a negative point charge? charge?

Field StrengthField Strength

• For a single point charge, electric field strength a distance r from the charge:

• E = kq/r2

• Units? • N/C

Calculate the electric field Calculate the electric field strength, 2m away from a strength, 2m away from a

3mC charge3mC charge

Force on a charge placed in Force on a charge placed in an E fieldan E field

• F = qE

• F = mg

Calculate the force on a Calculate the force on a 2mC charge, placed in an 2mC charge, placed in an electric field of strength electric field of strength

500N/C500N/C

Calculate the acceleration Calculate the acceleration of an electron (m = 9E-of an electron (m = 9E-31kg, q = 1.6E-19C), 31kg, q = 1.6E-19C), placed in a field of placed in a field of strength 3E-7 N/Cstrength 3E-7 N/C

A sphere (m = 2kg, q = A sphere (m = 2kg, q = 5mC) accelerates at 5mC) accelerates at

6m/s/s when placed in an 6m/s/s when placed in an electric field. Find the electric field. Find the

field strengthfield strength

• F = q1E = q1 (kq2/r2)

• F = kq1q2/r2

Fields Add Fields Add

• Imagine three charges, each with its own electric field

• At point P, E1 = 20N/C to the right, E2 = 10N/C to the left, and E3 = 15N/C to the right

• What is the net field at this point (assume right is +)?

Moving ChargesMoving Charges

• Imagine two positive charges, located 1.0m apart

• An outside force moves one charge 50 cm closer to the other

• What happens to the system?

• The system gains energy• What type?• Electric Potential Energy

• What happens if you let the charge go

• It moves to a lower energy state• Analogies to gravity?

Connections to E Fields?Connections to E Fields?

• Imagine a positive test charged, placed near a point charge

• As the test charge moves with the field lines (ie, in the direction of the arrows), what happens to its EPE?

• A negative test charge?

Field LinesField Lines

• Tell us the direction in which EPE decreases for a + charge

• Tell us the direction in which EPE increases for a - charge

• http://phet.colorado.edu/new/simulations/sims.php?sim=Charges_and_Fields

Which charge configuration Which charge configuration has the highest EPE?has the highest EPE?

• One way to think about the previous question: in which situation do you have to do more work to arrange the charges?

Statics to DyamicsStatics to Dyamics

• We’ll focus primarily upon situations where a charge’s EPE changes

• We’ve been discussing electrostatics (stationary charges)

• This EPE discussion gets us into the realm of electrodynamics (moving charges)

A Sense of ScaleA Sense of Scale

• Often times, we talk about groups of charge

• To deal with this, we talk about the amount of EPE/total charge

• We call this quantity, electric potential

Units?Units?

• Potential = EPE/charge• Units = J/C• 1 J/C = 1 Volt• Electric Potential is often called

voltage

Van de Graaff Voltage?Van de Graaff Voltage?

• A Van de Graaff is normally charged to thousands of volts, yet it won’t hurt you if you touch it

• Why then, can an outlet (V = 110V) really hurt you?

•Voltage = EPE/charge

• Voltage = EPE/charge

Connection to E Fields?Connection to E Fields?

• How does test charges electric potential change as it moves through a constnat E field?

• Let’s assume constant field strength to make life easy…

A Mathematical A Mathematical ExpressionExpression

• How does the change in potential relate to the field strength E?

• The distance moved, d?• V = Ed• This only works for constant E

Fields (we need to use calculus if E is not constant)

Voltage Difference on the Voltage Difference on the Van de Graaf?Van de Graaf?

• Let’s measure the length of a spark to find V between the Van de Graaff

• Knowing the electric field strength necessary to ionize air (1E6 N/m), we can find V

Energy Conservation with Energy Conservation with ChargeCharge

• A 3mC charge is travels through a potential difference of 110V

• How much KE does it gain as it travels through this potential difference?

• In a television, an electron travels through a potential difference of 32,000V

• How fast is it traveling when it strikes the television screen?

• When charges are in a region where a potential difference exists, what do they do?

• They move• The movement of charge is called

electric current• Units = C/s = Amperes (A)