Electricity, Magnetism and Light PHYSICS 208, Instructor: Olga Kocharovskaya Lectures 1,2 (Ch.21) Electric Charge and Electric Field 1. Introduction How to solve the problems? Four types of interactions 2. Electric Properties of the matter Two types of electric charge Conductors and Insulators Coulomb’s Law 3. Electric field

How to solve problems? Solve many before this one Solve it yourself Ask for hints but not for solution Discuss it with your friends Think about it before you go to sleep ( you may find a solution in your dream) Use symmetry of the problem Use superposition principle Do not surrender! Forget it (not for exam!), then try again Enjoy the solution!!!

How to make sure your answer is correct? Get a general (algebraic) solution Check the units of the answer, make sure you have units consistency Check limiting cases Check an order of magnitude, is it REASONABLE? ( the speed should not be greater then than that of the light in vacuum, a charge should not be smaller than that of electron, a distance is unlikely to be smaller than m in our course, etc.) Check the answer in the textbook

Four types of interactions 1.Gravity (between massive bodies) Planetary systems, Galaxies,Space trajectories Earth Weight: F=mg

2. Electromagnetic Interactions ( ELECTRICALLY CHARGED BODIES) Structure of ATOMS e e

Positive and negative Ions

Structure of the Molecules ee H2H2 Na + Cl - e e

Chemical reactions and biological processes Water is an excellent solvent due to the dipole character of its molecule

Modern Technologies: internet, telecommunications, nanotechnolgies, CD, DVD, lasers, cell phones,…

Large Hadron Collider (LHC) Counter propagating proton beams accelerated to 7x10 12 eV In search for a dark matter 27 km ring 4.Weak Interactions Hadrons ( proton, neutron,… ), colour charge 3.Strong Interactions Leptons (electron, muon, tau- lepton, neitrinos) lepton charge Interactions between elementary particles, using modern EM technologies

Electric Properties of the matter 1.Two types of charges: + and – (Ben Franklin,1740) glass plastic silk fur

2. Quatization of charge Q=ne, n=1,2,3,… e is the minimum value of charge Particle mass charge electron 9.11× kg -1.60× C (-e) proton 1.672× kg +1.60× C (+e) neutron 1.674× kg 0 SI : [Q]=1C

3. Conservation of Charge: ee Na Cl Na + Cl - e e Na + q 1 =e Cl - q 2 =-e q 1 =0 q 2 =0 q 1 +q 2 =0

4. Three types of materials 1. Conductors (free electrons) Metalls, alloys, plasmas Induction 2. Insulators=Dielectrics (bounded electrons) Glass, plastic, paper Polarization 3. Semiconductors (number of free electrons strongly depends on external conditions such as temperature, electric field, pressure; under the usual conditions number of electrons is small)

5. Amber effect : Charged and neutral object always attract each other

6. Charging of neutral objects 1.By friction: q 1 =0, q 2 =0 q 1 =Q q 2 =-Q 2. By contact q 1 =Q q 2 =0 q 1 +q 2 =Q q 1 =Q/2 q 2 =Q/2 3. By induction

Coulomb’s Law, 1786

Coulomb’s Law For an ensemble of charges use a Superposition Principle:

Example1. Compare the electric and gravity forces between an electron and a proton.

Electric Field, “That one body may act upon another at a distance … is to me so great an absurdity…” I. Newton Michael Faraday ( ) Two steps: 1.Q creates electric field, 2. produces the force on q Coulomb’s LawNewton’s Law r r or QM q m

Two steps in more details: the source and test charges Q Source Q produces electric field at point P indepententely on the presence of charge q at this point: produces a force on a test charge q: SI units of E: [E]=[F]/[q]=N/C

of a point charge For charged bodies of finite size at r ∞

E of a dipole: along x axis -q+q x0 -a x-a a x+a

E of a dipole : along y axis q-q -a a y

Field of a line of charge ( along the line) dq z

E of a half of the ring of charge dq dE E tot dE y dE

(near the disc it looks like an infinite plane)

Two infinite planes

Electric field lines 1.Tangent is in direction of 2.Density of lines is proportional to |E| 3. Originate on “+” and terminate on “-” charges 4. Crossing of E lines is impossible 5. Closed lines are impossible in ES NB: in the general case (i)|E| is not const along E lines (ii)Not the trajectories of the charged particles

A positive vs. negative point charge

of a dipole

Infinite line of charge

Two infinite planes Uniform E : the same direction and magnitude at each point N=const, S=const, E=const

Motion in a uniform E - + v0v0 e E Data: electron,, L,v 0 Find: 1.trajectory; 2.v f F vfvf parabola

Electric dipole in a uniform E 1.Stable equilibrium 2.Unstable equilibrium