Electrostatics Chapter 23 Week-1-2

Electricity Probable First Observation Electricity

Idiot! If lightening had actually traveled down the kite string, old Ben Franklin would have been toast! Probably never happened, but good story!

A Quick Experiment

Experimental Procedure Pivot The sequence of Experiments 1.Identify the two rods 2.Treat each rod 3.Bring one rod near to the other 4.PREDICT WHAT WILL HAPPEN 5.VOTE ON POSSIBILITIES 6.Observe what happens 7.Did you learn anything? What?

Allowable Predictions (Use your clicker if you have one.) A. Rods will attract each other B. Rods will repel each other C. Nothing will happen D. Something not listed above will happen

Experiment #1 Pivot motion Rubber rod A. Rods will attract each other B. Rods will repel each other C. Nothing will happen D. Something not listed above will happen

Experiment #2 Pivot Rubber rubbed with skin of dead rabbit Rubber rubbed with skin of dead rabbit A. Rods will attract each other B. Rods will repel each other C. Nothing will happen D. Something not listed above will happen

The charges on the two rods are.. A. Since we treated both rods in the same way, they should be of the same type B. ……. different types C. I have no idea what you are asking for. D. Leave me alone … I’m napping!

If you rubbed the rods longer and/or harder, do you think the effect that you see would be A. Stronger B. Weaker C. The same

If the two rods are brought closer together, the force acting between them will get … A. Stronger B. Weaker C. The same

Definition of sorts We DEFINE the “stuff” that we put on the rods by the rubbing process as CHARGE. We will try to understand what charge is and how it behaves. We add to the properties of materials: MassCharge

Experiment #3 Pivot Glass rubbed with wool A. Rods will attract each other B. Rods will repel each other C. Nothing will happen D. Something not listed above will happen Glass rubbed with wool

Experiment #4 Pivot 1. Rods will attract each other 2. Rods will repel each other 3. Nothing will happen 4. Something not listed above will happen Glass rubbed with wool Rubber rubbed with skin of dead rabbit

What’s Going On? All of these effects involve rubbing two surfaces together. Or pulling two surfaces apart. Something has “happened “to each of these objects. These objects have a new PROPERTY Other properties are mass, color We call this NEW PROPERTY.………. ……… CHARGE. There seems to be two types of charge.

We call these two types of charge Positive Negative NEUTRAL. An object without either a (+) or (-) charge is referred to as being NEUTRAL.

Example - Tape

Separation

An Example

Effect of Charge

We have also observed that there must be TWO kinds of charge. Call these two types positive (+) negative(-) We “define” the charge that winds up on the rubber rod when rubbed by the dead cat to be NEGATIVE. The charge on the glass rod or the dead cat is consequently defined as POSITIVE.

Old Ben screwed up more than once!!

From whence this charge ??? -+-+ Easily Removed

Materials Two kinds of materials: Insulators Electrons and Protons are tightly bound to their positions. Hard to move them around. Conductors Electrons are easily removed and moved around. Electrons are said to be MOBILE charges. There are other kinds of materials that we will not discuss: semiconductors, semi-metals

Pivot Experiment #5 Rubber rubbed with skin of dead rabbit Metal Rod A. Rods will attract each other B. Rods will repel each other C. Nothing will happen D. Something not listed above will happen

What about a charged rod and a piece of wood?? A. Rods will attract each other B. Rods will repel each other C. Nothing will happen D. Something not listed above will happen

Ways to charge an object Rubbing or bond breaking (same thing) Transfer Direct transfer Polarization Induction

Neutral Object - POLARIZATION Positive charge attracts negative charges. Rod becomes “polarized. Negative end is closer to positive charge Distance effect causes attraction.

Induction

Polarize

Ground

Remove Ground

Positive !

Balloon Physics

Same as before: Polarization

What happens when two surfaces touch or rub? Bonding!

The Triboelectric Series No! When two of the following materials are rubbed together under ordinary circumstances, the top listed material becomes positively charged and the lower listed material becomes negatively charged. MORE POSITIVE rabbit's fur glass mica nylon wool cat's fur silk paper cotton wood acrylic cellophane tape polystyrene polyethylene rubber balloon saran wrap MORE NEGATIVE No!

So far we have found? There are TWO types of charge. Positive Negative Like Charges Attract Un-Like charges repel The force between charges increases as they are brought closer together. This charge separation results from chemical bonds which are severed.

Forces Between Charges Q1Q1 Q2Q2 AttractRepel ++X +-X -+X --X

Coulomb’s Law – Force between charges The force between two charges is proportional to the product of the two charges and inversely proportional to the square of the distance between them. The force acts along the line connecting the two charges.

Remember

Coulomb’s Law The Unit of Charge is called THE COULOMB Smallest Charge: e ( a positive number) 1.6 x Coul. electron charge = -e Proton charge = +e

Three point charges are located at the corners of an equilateral triangle as shown in Figure P23.7. Calculate the resultant electric force on the 7.00-μC charge.

Two small beads having positive charges 3q and q are fixed at the opposite ends of a horizontal, insulating rod, extending from the origin to the point x = d. As shown in Figure P23.10, a third small charged bead is free to slide on the rod. At what position is the third bead in equilibrium? Can it be in stable equilibrium?

The Electric Field

Fields Imagine an object is placed at a particular point in space. When placed there, the object experiences a force F. We may not know WHY there is a force on the object, although we usually will. Suppose further that if we double some property of the object (mass, charge, …) then the force is found to double as well. Then the object is said to be in a force field. The strength of the field (field strength) is defined as the ratio of the force to the property that we are dealing with.

Example – Gravitational Field. Property is MASS (m). Force is m g. Field strength is defined as Force/Property

The Gravitational Field That We Live In. m M mgmg MgMg

This is WAR You are fighting the enemy on the planet Mongo. The evil emperor Ming’s forces are behind a strange green haze. You aim your blaster and fire … but …… Ming the merciless this guy is MEAN !

Nothing Happens ! The Green thing is a Force Field ! The Force may not be with you ….

Side View The FORCE FIELD Force Position o |Force| Big!

Properties of a FORCE FIELD It is a property of the position in space. There is a cause but that cause may not be known. The force on an object is usually proportional to some property of an object which is placed into the field.

Mysterious Force F

Electric Field If a charge Q is in an electric field E then it will experience a force F. The Electric Field is defined as the force per unit charge at the point. Electric fields are caused by charges and consequently we can use Coulombs law to calculate it. For multiple charges, add the fields as VECTORS.

Two Charges

Doing it Q r q A Charge The spot where we want to know the Electric Field F

General-

Force  Field

Two Charges What is the Electric Field at Point P?

The two S’s S uperposition S ymmetry

What is the electric field at the center of the square array?

Kinds of continuously distributed charges Line of charge  or sometimes = the charge per unit length. dq=  ds (ds= differential of length along the line) Area  = charge per unit area dq=  dA dA = dxdy (rectangular coordinates) dA= 2  rdr for elemental ring of charge Volume  =charge per unit volume dq=  dV dV=dxdydz or 4  r 2 dr or some other expressions we will look at later.

Continuous Charge Distribution

ymmetry

Let’s Do it Real Time Concept – Charge per unit length  dq=  ds

The math Why?

A Harder Problem A line of charge  =charge/length setup dx L r   x dEdE dE y

(standard integral)

Completing the Math 1/r dependence

Dare we project this?? Point Charge goes as 1/r 2 Infinite line of charge goes as 1/r 1 Could it be possible that the field of an infinite plane of charge could go as 1/r 0 ? A constant??

The Geometry Define surface charge density  =charge/unit-area dq=  dA dA=2  rdr (z 2 +r 2 ) 1/2 dq=  x dA = 2  rdr

(z 2 +r 2 ) 1/2 

Final Result

Look at the “Field Lines”

What did we learn in this chapter?? FIELD We introduced the concept of the Electric FIELD. We may not know what causes the field. (The evil Emperor Ming) If we know where all the charges are we can CALCULATE E. E is a VECTOR. The equation for E is the same as for the force on a charge from Coulomb’s Law but divided by the “q of the test charge”.

What else did we learn in this chapter? We introduced continuous distributions of charge rather than individual discrete charges. Instead of adding the individual charges we must INTEGRATE the (dq)s. There are three kinds of continuously distributed charges.

Kinds of continuously distributed charges Line of charge  or sometimes = the charge per unit length. dq=  ds (ds= differential of length along the line) Area  = charge per unit area dq=  dA dA = dxdy (rectangular coordinates) dA= 2  rdr for elemental ring of charge Volume  =charge per unit volume dq=  dV dV=dxdydz or 4  r 2 dr or some other expressions we will look at later.

The Sphere thk=dr dq=  dV=  x surface area x thickness =  x 4  r 2 x dr dq

Summary (Note: I left off the unit vectors in the last equation set, but be aware that they should be there.)

To be remembered … If the ELECTRIC FIELD at a point is E, then E = F /q (This is the definition!) Using some advanced mathematics we can derive from this equation, the fact that: