Electrostatics

Lessons 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” Reflects relative number of electrons in a substance Conserved Units of Coulombs (C) An electron has a charge of 1.6 x C of charge

Significant Charge Amounts When we rub balloons on rabbit hair in the lab, we’re generating 10’s of  C

Which of the following will tell you without a doubt that an object 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 from the ceiling. All three are charged with various materials. It is found that 1 and 2 repel one another, and 2 and 3 repel one another. From this, we can 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 from the ceiling. Two of the three are then charged with various materials. It is found that 1 and 2 attract one another, and 2 and 3 repel one another. From this, we can 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

Which spheres experience the greatest attraction?

Methods of Charging

Charging by Friction ns/sims.php?sim=John_Travoltagehttp://phet.colorado.edu/new/simulatio ns/sims.php?sim=John_Travoltage

Charging by Induction ns/sims.php?sim=Balloons_and_Static_ Electricityhttp://phet.colorado.edu/new/simulatio ns/sims.php?sim=Balloons_and_Static_ Electricity

Charge 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? Both positive and negative charges are still in a substance Why is it attracted?

Charging by Contact/Conduction The physical movement of charge from one object to another

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

Lightning

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 Law Coulomb’s Law gives us a way to calculate the force between two charged objects F E = kq 1 q 2 /d 2 k is a constant = 8.99 x 10 9 N m 2 /C 2

Similarities to Gravity Recall how we calculated the gravitational force between objects: F G = Gm 1 m 2 /d 2 G is a constant = 6.67 x N m 2 /kg 2 Look familiar?

Different 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 +6  C charge and a -5  C 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

Levitation 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 below. Which charge would exert the greatest force on the -2 charge?

Which list below ranks the charges in order of increasing force on the -2 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 net force on the -2 charge?

Electric 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 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 charge

Which diagram correctly illustrates the field surrounding a negative point charge?

Field Strength For a single point charge, electric field strength a distance r from the charge: E = kq/r 2 Units? N/C

Calculate the electric field strength, 2m away from a 3mC charge

Force on a charge placed in an E field F = qE F = mg

Calculate the force on a 2mC charge, placed in an electric field of strength 500N/C

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

A sphere (m = 2kg, q = 5mC) accelerates at 6m/s/s when placed in an electric field. Find the field strength

F = q 1 E = q 1 (kq 2 /r 2 ) F = kq 1 q 2 /r 2

Fields Add Imagine three charges, each with its own electric field At point P, E 1 = 20N/C to the right, E 2 = 10N/C to the left, and E 3 = 15N/C to the right What is the net field at this point (assume right is +)?

Moving 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? 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 Lines Tell us the direction in which EPE decreases for a + charge Tell us the direction in which EPE increases for a - charge

ns/sims.php?sim=Charges_and_Fieldshttp://phet.colorado.edu/new/simulatio ns/sims.php?sim=Charges_and_Fields

Which charge configuration 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 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 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? Potential = EPE/charge Units = J/C 1 J/C = 1 Volt Electric Potential is often called 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

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 Expression 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 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 Charge 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)