Physics 1202: Lecture 3 Today’s Agenda Announcements: –Lectures posted on: –HW assignments, solutions etc. Homework #1:Homework #1: –On Masterphysics today: due next Friday –Go to masteringphysics.com and register –Course ID: MPCOTE62465 Labs: Begin in two weeks No class Monday: Labor Day

Today’s Topic : End of Chapter 15 –Review Electric Field of a point charge –Electric Field of an electric dipole –Other geometries –Conductors and insulators –Moving charges: Use Newton’s law

Review of E for a point charge Q The Old Way: Vector Maps Lines leave positive charges and return to negative charges Number of lines leaving/entering charge = amount of charge Tangent of line = direction of E Density of lines = magnitude of E + O A New Way: Electric Field Lines + chg - chg + O  O 

 x y a a +Q -Q r Electric Dipole E E Symmetry E x = ?? E y = ?? Calculate for a pt along x-axis: (x,0) What is the Electric Field generated by this charge arrangement?

Electric Dipole: Field Lines Lines leave positive charge and return to negative charge E x (x,0) = 0 What can we observe about E? E x (0,y) = 0 Field largest in space between the two charges We derived (y=a):... for r >> a,

Field Lines from 2 Like Charges Note the field lines from 2 like charges are quite different from the field lines of 2 opposite charges (the electric dipole) There is a zero halfway between charges r>>a: looks like field of point charge (+2q) at origin.

Lecture 3, ACT 1 Consider a dipole aligned with the y-axis as shown. –Which of the following statements about E x (2a,a) is true? +Q x y a a -Q a 2a (a) E x (2a,a) < 0 (b) E x (2a,a) = 0(c) E x (2a,a) > 0 q1q1 q2q2

Electric Dipole Summary x y a a +Q -Q Case of special interest: (antennas, molecules) r > > a r Along y-axis  Er Qa r y ,   Along x-axis  Er Qa r y,   Along arbitrary angle  dipole moment with

Geometries: Infinite Line of Charge Solution: - symmetry: E x =0 - sum over all elements The Electric Field produced by an infinite line of charge is: –everywhere perpendicular to the line – is proportional to the charge density –decreases as 1/r x y xx r' r  EE qq = Q / L : linear charge density

Lecture 3, ACT 2 Consider a circular ring with a uniform charge distribution ( charge per unit length) as shown. The total charge of this ring is +Q. The electric field at the origin is (a) zero R x y (b) (c)

Geometries: Infinite plane Solution: - symmetry: E x =E y =0 - sum over all elements The Electric Field produced by an infinite plane of charge is: –everywhere perpendicular to the plane –is proportional to the charge density –is constant in space !  = Q/A : surface charge density y z xx r' r  EE qq x yy

Two infinite planes Same charge but opposite Fields of both planes cancel out outside They add up inside Perfect to store energy !

Summary Electric Field Distibutions Dipole ~ 1 / r 3 Point Charge ~ 1 / r 2 Infinite Line of Charge ~ 1 / r Infinite Plane of Charge constant

Motion of Charged Particles in Electric Fields Remember our definition of the Electric Field, And remembering Physics 1201, Now consider particles moving in fields. Note that for a charge moving in a constant field this is just like a particle moving near the earth’s surface. a x = 0 a y = constant v x = v ox v y = v oy + at x = x o + v ox ty = y o + v oy t + ½ at 2

Motion of Charged Particles in Electric Fields Consider the following set up, e-e- For an electron beginning at rest at the bottom plate, what will be its speed when it crashes into the top plate? Spacing = 10 cm, E = 100 N/C, e = 1.6 x C, m = 9.1 x kg

Motion of Charged Particles in Electric Fields e-e- v o = 0, y o = 0 v f 2 – v o 2 = 2a  x Or,

Insulators vs. Conductors Insulators – wood, rubber, styrofoam, most ceramics, etc. Conductors – copper, gold, exotic ceramics, etc. Sometimes just called metals Insulators – charges cannot move. –Will usually be evenly spread throughout object Conductors – charges free to move. –on isolated conductors all charges move to surface.

E E Conductors vs. Insulators E E E in = 0 E in < E

Hollow conductors

Conductors & Insulators How do the charges move in a conductor?? Hollow conducting sphere Charge the inside, all of this charge moves to the outside. Consider how charge is carried on macroscopic objects. We will make the simplifying assumption that there are only two kinds of objects in the world: Insulators.. In these materials, once they are charged, the charges ARE NOT FREE TO MOVE. Plastics, glass, and other “bad conductors of electricity” are good examples of insulators. Conductors.. In these materials, the charges ARE FREE TO MOVE. Metals are good examples of conductors.

Conductors vs. Insulators

Charges on a Conductor Why do the charges always move to the surface of a conductor ? –E = 0 inside a conductor when in equilibrium (electrostatics) ! »Why? If E  0, then charges would have forces on them and they would move ! Therefore, the charge on a conductor must only reside on the surface(s) ! Infinite conducting plane Conducting sphere

Homework #1 on Mastering Physics –From Chapter 15 Recap of today’s lecture Electric Field Lines Examples: Dipole, line, surface, two parallel plates Charges moving in electric field Conductors / insulators