# Physics For Engineers and Scientists II

Electrostatics Chapter 23 Week-1-2 Whats Happening Clicker use will start on Friday (maybe). Today we begin the study of charge with make-believe clickers. There will NOT be a quiz this week. There WILL be a quiz a week from Friday.

WebAssigns are now active. 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 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 we learn anything? Pivot

Allowable Predictions In the future we will use clickers for this. 1. Rods will attract each other 2. Rods will repel each other 3. Nothing will happen 4. Something not listed above will happen Experiment #1 Rubber rod

Pivot Rubber rod 1. 2. 3. 4. Rods will attract each other Rods will repel each other Nothing will happen

Something not listed above will happen Experiment #2 Rubber rubbed with skin of dead rabbit Pivot Rubber rubbed with skin of dead rabbit 1.

2. 3. 4. Rods will attract each other Rods will repel each other Nothing will happen Something not listed above will happen Experiment #3 Glass rubbed with wool

Pivot Glass rubbed with wool 1. 2. 3. 4. Rods will attract each other Rods will repel each other

Nothing will happen Something not listed above will happen What is the effect of DISTANCE?? Experiment #4 Rubber rubbed with skin of dead rabbit

Pivot Glass rubbed with wool 1. 2. 3. 4. Rods will attract each other Rods will repel each other Nothing will happen

Something not listed above will happen Whats 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. Example - Tape Separation Another 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. From whence this charge??? Easily Removed + Materials Two kinds of materials:

Insulators Conductors

Electrons and Protons are tightly bound to their positions. Hard to move them around. 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 Experiment #5 Rubber rubbed with

skin of dead rabbit Pivot Metal Rod 1. 2. 3. 4. Rods will attract each other Rods will repel each other

Nothing will happen 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 From WebAssign Three objects are brought close to each other, two at a time. When objects A and B are brought together, they attract.

When objects B and C are brought together, they repel. From this, we conclude which of the following? (Select all that apply.) [_] Objects A and C possess charges of the same sign. [_] All three of the objects possess charges of the same sign. [_] One of the objects is neutral. [_] Objects A and C possess charges of opposite sign. [_] We need to perform additional tests to determine information about the charges on the object What happens when two

surfaces touch or rub? Bonding! The Triboelectric Series 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. No! No! No! No!

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 Summary - Rubbings What have we 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 Q1

Q2 + + + - X

- + X - - Attract

Repel X X Coulombs 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. q1q2 1 q1q2 q1q2 F 2 k 2 2 r 4 0 r r 1

k 4 0 Remember Coulombs Law The Unit of Charge is called THE COULOMB 1 q1q2 F runit

2 4 0 r 1 k 9 x109 Nm 2 / C 2 4 0 Smallest Charge: e ( a positive number) 1.6 x 10-19 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-C 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 mg. Field strength is defined as Force/Property F mg Gravitational Field Strength Force Gravitational Force mg g

Property mass m The Gravitational Field That We Live In. M m mg Mg

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

Nothing Happens! The Green thing is a Force Field! The Force may not be with you . Side View The FORCE FIELD Force |Force|

o Big! Position 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 F 1 qq0 q

E k 2 runit k 2 runit q0 q0 r r Doing it qQ F k runit 2 r F Q

E k 2 runit q r F q Q A Charge r

The spot where we want to know the Electric Field GeneralqQ F k 2 runit r F Q E k 2 runit q r General

Fj Qj E E j k 2 r j ,unit q rj Force Field Two Charges What is the Electric Field at Point P?

The two Ss Superposition Symmetry 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= 2rdr for elemental ring of charge

Volume =charge per unit volume dq=dV dV=dxdydz or 4r2dr or some other expressions we will look at later. Continuous Charge Distribution ymmetry Lets Do it Real Time Concept Charge per

unit length dq= ds The math ds rd E y 0 Why? 0 dq

E x ( 2) k 2 cos( ) r 0 0 rd E x ( 2) k 2 cos( ) r 0 2k Ex r

0 2k cos( )d sin( 0 ) r 0 A Harder Problem setup dE

dEy r x A line of charge =charge/length

L dx L 2 E x k dx cos( ) (r

2 L 2 cos( ) x2 ) r

2 2 (r x ) L/2 rdx E x 2k 2 2 3/ 2 (

r x ) 0 L/2 dx E x 2kr 2 2 3/ 2 ( r

x ) 0 (standard integral) Completing the Math Doing the integration : kL Ex L2 2

r r 4 In the limit of a VERY long line : L L2 r 4 kL 2k Ex r

L r 2 2 1/r dependence Dare we project this?? Point Charge goes as 1/r2 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/r0? A constant?? The Geometry Define surface charge density =charge/unit-area (z2+r2)1/2 dq=dA dA=2rdr dq= x dA = 2rdr

dq cos( ) k 2rdr z dE z k 2 2 2 z r z r2 z2 r2

(z2+r2)1/2 R

E z 2kz 0 z rdr 2 r 2 3/ 2

1/ 2 Final Result (z2+r2)1/2 z

1 E z z2 R2 2 0 When R , Ez 2 0

Look at the Field Lines What did we learn in this chapter?? We introduced the concept of the Electric FIELD. 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 Coulombs 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= 2rdr for elemental ring of charge

Volume =charge per unit volume dq=dV dV=dxdydz or 4r2dr or some other expressions we will look at later. The Sphere dq thk=dr dq=dV= x surface area x thickness = x 4r2 x dr

Summary qQ F k 2 runit r F Q E k 2 runit q r General Fj

Qj E E j k 2 r j ,unit q rj dV ( r ) E k r

2 dA(r ) k r 2 ds (r )

k r2 (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: F qE

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