PHYS 219 Fall semester 2014 Lecture 02: Coulomb’s law & Interaction of point charges Dimitrios GIANNIOS Physics & Astronomy Department Purdue University

Electric, Magnetic phenomena and light: Electromagnetic Theory this lecture Charge Q Electric field E Electric force FE Current I=Qv Magnetic field B Magnetic Force FB F=mα

Observational Facts Discovery of electricity is generally credited to the Greeks About 2500 years ago They observed electric charges and the forces between them in many situations Used amber A type of dried tree sap After amber is rubbed with a piece of animal fur, the amber can attract small pieces of dust

Observational Facts, cont. The Greek word for amber was “elektron” from which we get the words electron and electricity Modern experiments use plastic and paper The force occurs even when the plastic and paper are not in contact

Basic Properties of Charges There are two types of electric charges They are called positive and negative Protons have positive charges Electrons have negative charges Charge comes in quantized units All protons carry the same amount of charge, +e All electrons carry the same amount of charge, -e

Basic Properties, cont. Like charges repel each other, unlike charges attract Like charges – both positive or both negative Unlike charges – one positive and one negative The “like” and “unlike” apply to the signs of the charges, not their magnitudes

Basic Properties, final Charge is conserved The total charge on an object is the sum of all the individual charges carried by the object Charge can move from place to place, and from one object to another, but the total charge of the universe does not change

What is Electric Charge? Charge is a fundamental property of matter The amount of charge on a particle determines how the particle reacts to electric and magnetic fields The SI unit of charge is the Coulomb Electron charge = -e = -1.6 x 10-19 C Proton charge = +e = +1.6 x 10-19 C neutron charge = 0 symbol e: the magnitude of the charge on an electron or proton q and Q: charge in general

How do objects become charged? The addition or removal of electrons creates negatively and positively charged objects Except under extreme conditions, protons stay in place and electrons move What is total charge on this nanoparticle? Ans:Qtot =3xe-=3x(-1.6x10-19 C)=-4.8x10-19 C - = 1e- - - + = 1p - - How was a net charge on this object created? + - + -

A fun example - + - - - + - - + - - - - - balloon Approach wall fur - -- friction + - - - + - - - + balloon - - - + - - - - - + - - + - - - + ++ wall Rub balloon with fur

Electric Forces and Coulomb’s Law Electric force can be attractive or repulsive Assume two charged particles can be modeled as point particles The magnitude of the electric force between the two particles is given by Coulomb’s Law

Coulomb’s Law Coulomb’s Law says the magnitude of the force between two electric charges is given by The constant k = 9 x 109 N . m2 / C2 The direction of the force is along the line that connects the two charges A repulsive force will give a positive value for FE Between like charges An attractive force will give a negative value for FE Between unlike charges

Features of Coulomb’s Law The form of Coulomb’s Law is similar to Newton’s Law of Gravity Both laws exhibit a 1/r2 dependence on the separation between particles A negative charge can move in a circular orbit around a positive charge This was the early model for the atom Gravity is always attractive Electric forces may be attractive or repulsive

Features of Coulomb’s Law, cont. The value of FE given by Coulomb’s Law is the magnitude on each of the particles A force of FE is exerted on q1 and a force of equal magnitude and opposite direction is exerted on q2 Newton’s Third Law action-reaction pair but acting from a distance!

How strong is the electric force? Assume you have two boxes, 1m apart, each containing one gram of electrons (me = 9 x 10-28 gr) There would be N=1.1 x 1027 electrons in each box: total charge Q = N x e- ≈ -1027 x 10-19 C = -108 C This is almost a million times larger than the force between the Sun and the Earth!!! Ordinary matter consists of approximately equal numbers of electrons and protons With equal numbers, Qtotal = 0 and FE = 0

Principle of Superposition Q: Since Coulomb’s Law only involves TWO point charges, what do you do when more than two point charges are present at one time? A: Since force is a vector, the total force exerted on a particular charge is the vector sum of all the individual forces acting on that charge. This is often called the Principle of Superposition

The Addition of vectors (graphical) Total (net) Force:

Addition of vectors (numerical) 1. analyze each vector to its components y y θ x x 2. Add the vector components along each direction

Example of total force calculation numerical input: α = 10 cm = 0.1 m, q1= |q2| = q3 = 1μC = 10-6 C π/4 π/2 Step 1: Units! π/4 Step 2:Geometry! y Step 3: Force Diagram 45o x q3

Example of total force calculation y Step 4: Vector Components 45o x Step 5: Force Magnitude: Coulomb’s Law Step 6: Add vector components