Physics 1202: Lecture 3Today’s Agenda

• Announcements:– Lectures posted on:

www.phys.uconn.edu/~rcote/– HW assignments, solutions etc.

• Homework #1:Homework #1:– On Masterphysics today: due next FridayOn 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

EE

Symmetry

Ex = ?? Ey = ??

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 chargeand return to negative charge

• Ex(x,0) = 0

What can we observe about E?

• Ex(0,y) = 0

• Field largest in space betweenthe 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 Ex(2a,a) is true?

+Q

x

y

a

a-Q

a

2a

(a) Ex(2a,a) < 0 (b) Ex(2a,a) = 0 (c) Ex(2a,a) > 0

q1 q2

Electric Dipole Summary

x

y

a

a

+Q

-Q

Case of special interest:

(antennas, molecules)

r > > a

r

• Along y-axis

E rQa

ry 0 4

14 0

3,

• Along x-axis

E rQa

ry ,0 2

14 0

3

• Along arbitrary angle dipole moment

with

Geometries: Infinite Line of Charge• Solution:- symmetry: Ex=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

r'r

E

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: Ex=Ey=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

r'

r

E

q

x

++++++++++++++++y

Two infinite planes• Same charge but opposite

• Fields of both planes cancel out outside

• They add up inside

++++++++++++++++++++++++++

- - - - - - - - - - - - - - - - - - - - - - - - - -

Perfect to store energy !

SummaryElectric Field Distibutions

Dipole

~ 1 / r3

Point Charge

~ 1 / r2

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.

ax = 0 ay = constant

vx = vox vy = voy + at

x = xo + voxt y = yo + voyt + ½ at2

Motion of Charged Particles in Electric Fields

• Consider the following set up,

++++++++++++++++++++++++++

- - - - - - - - - - - - - - - - - - - - - - - - - - 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 10-19 C, m = 9.1 x 10-31 kg

Motion of Charged Particles in Electric Fields

++++++++++++++++++++++++++

- - - - - - - - - - - - - - - - - - - - - - - - - - e-

vo = 0, yo = 0

vf2 – vo

2 = 2ax

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

Ein = 0 Ein < 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 conductingplane

++++++++++++

++++++++++++

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