phys 212 lecture 03pre-electric fields

PHYS 212 Lecture 03 1/21/2014 Dr. Stephen J. Van Hook, Penn State Univ

PHYS 212 Lecture 03: Electric Fields

From Today’s Reading, you should have learned:

Did you register your clicker? (Is its code set to AD?)Are your notes out & phone put away?

1. Do Electric fields point towards or away from + charges? - charges?

3. How do Electric field lines relate to electric field vectors?

2. What is an electric dipole, what is the electric dipole moment (what direction does it point)?

4. What is linear charge density and how do you calculate E for a continuous line of charge?


Big Concepts & Skills for Today:

1. What is the electric field?

2. How electric charges respond to an E field.

3. How to interpret/draw E field vectors & E field lines.

4. What is an electric dipole (the simplest charge distribution)?

5. How to find the E field of continuous charge distributions.Objective #9: Calculate the electric field from a discrete or continuous

distribution of charges (using vectors, symmetry and calculus as appropriate) and draw the electric field lines corresponding to the electric field. (Coulomb’s Law)

Objective #10: Determine the force and/or torque on an electric charge or collection of electric charges (e.g., a dipole) due to an electric field.


The Electric FieldElectric Field Vector Representations:

Direction & Magnitude

Field Line Representation

Created using PhET simulation Charges and Fields

+


Gravitational field created by M:

Field is felt by m

In using a gravitational field, we separate the creation of the field from the effect of the field

Gravitational field due to M has effect on m:

m

m

m also creates a gravitational field that is felt by M!(masses only feel fields created by other masses, not themselves)

M


Electric field created by Q:

Field is felt by q

In using an electric field, we separate the creation of the field from the effect of the field

Electric field from Q has an effect on q:

q also creates an electric field that is felt by Q!(charges only feel fields created by other charges, not themselves)

~E =~FE

q=

kQq/r2

qr̂ = k

Q

r2r̂

~FE = q ~E

Units: N/C

+

+Q

q q

q


Mass M! ! Charge Q (±)

Create Field:

Field exerts forces on other masses/charges:

Source of Field:

Why bother inventing the field idea at all? (1) fields can have energy and momentum [light!](2) gives mechanism for action at a distance without v > c(3) other mechanisms for creating electric field than charges!

Know what creates each kind of field and what objects feel the effect of the field

~g = �GM

r2r̂ ~E = k

Q

r2r̂

~Fg = m~g ~FE = q ~E


Don’t confuse the field created by a charge and the field experienced by a charge

+

Field created by charge Field experienced by charge

+

From the context, you’ll have to figure out which it isPHYS 212 Lecture 03 1/21/2014 Dr. Stephen J. Van Hook, Penn State Univ

Draw the electric force vectors on the q’s due to this E field

Field Line Representation


+q

+q

+q

-2q

-q -q+2q

Treat the q’s as infinitessimal test charges


E = 0 at any equilibrium position*

Signs of charges?Which has larger |q|?

Where is the equilibrium (E = 0) position?

*if FE only force

Stable or unstable?


Note: these arrows indicate direction only


Electric field lines:1. have direction tangent to E field at every point 2. start on positive charges (sources) or infinity3. end on negative charges (sinks) or infinity4. # of field lines on charge proportional to magnitude of charge5. never cross each other [why not?]6. are generally denser where the field is stronger

Electric field lines indicate direction and rough estimate of relative magnitude of E field

+ -

dipole

+ -


What information can we extract from this field line diagram?


What information can we extract from this field line diagram? How is it different from the previous one?

Far from the charges, the field is either:

Dipole or higher order “pole” Monopole

net charge - lines going radially

inwards/outwards

zero net charge - all lines

loop back

quadrupole

PHYS 212 Lecture 03 1/21/2014 Dr. Stephen J. Van Hook, Penn State Univ PHYS 212 Lecture 03 1/21/2014 Dr. Stephen J. Van Hook, Penn State Univ

Don’t confuse field vectors and field lines

Field lines extend over space - E is

tangent to the lines & density tells you

magnitude of E

A field vector tells you E at a point in space.

+


Know what to look for in a field line diagram

Do lines go out to / in

from infinity?

Do lines go from one charge to

another?

Is there a place the field lines avoid going?

(“saddle point”)

+


Can you decode this field line diagram?


If the charge in the center of the below diagram is q, what is the charge above it?

First answer qualitatively (bigger or smaller, same sign or opposite)

then quantitatively

q

q2

Can you decode this field line diagram?


The dipole: An important special charge distribution

Zero net charge (equal & opposite charges separated)

+

-

d

q

-q


Dipole moment p is a vector pointing from - to + charge

Common arrangement in Nature: diatomic molecules (e.g., CO, NO, HCl etc.)

Neutral since qnet = 0

An electric dipole* has 2 equal but opposite q’s and is characterized by a dipole moment p = qd

+

-

d p = qd

q

-q

*a monopole is a just point charge

HRW: Fundamentals of Physics

+

-

p

Has axial symmetry around axis defined by p (usually set to be the z-axis)


HRW: Fundamentals of Physics

+

-

p

The E fields created by the + and - charges partially cancel one another

Direction of Ez above & below

dipole?

Direction of Ez “inside” dipole

(between charges)?

Field far from charges (r >> d)?

x

~E = ~E+q + ~E�q


E of a dipole decays faster than 1/r2 since the separation of the charges becomes negligible

z

x

~E = ~E+q + ~E�q

~E ⇡ 2k~p

|z|3

Far away (r >> d), the separation of the charges is negligible, so the field rapidly decays in magnitude.

Field along dipole (z) axis:

see textbook for derivation

even off axis: E ⇠ kp

r3


Now let’s spread charge out (like peanut butter on bread) so we’re not looking at point charges, but continuous charge distributions

The dimension & geometry are importantWe can only do some simple, symmetric geometries

without really ugly mathematics...

QQ

Need to work with the charge density (thickness of the peanut butter spread) to analyze the problem

� =Q

L⌘ =

Q

A⇢ =

Q

V

spread Q


To calculate E of a continuous charge distribution Q, divide up Q into many infinitessimal charges dq

Find field dE at P due to dq and sum all dEs to get E

Q =X

i

�qi =

Zdq

~E =X

i

k�q

r2ir̂i !

Zkdq

r2r̂

� ~E = k�q

r2r̂ ! d ~E = k

dq

r2r̂r

Δq

r̂

P

Q


dQ

-q outside: get exact same result as if entire charge Q were located at the center of the shell!

uniform shell of charge Q

-q Q

The same shell rules from Newton’s Law of Gravity also apply to Coulomb’s Law for electric fields


dQuniform shell of charge Q

-q

-q inside: net electric force on -q is 0 (all

the forces from the dQ’s exactly

cancel)!

The same shell rules from Newton’s Law of Gravity also apply to Coulomb’s Law for electric fields

since no force on -q, E = 0 at that point

(i.e., anywhere inside)


each sphere/shell has the same charge Q

I IIIII

P PP

uniformly charged sphereshell

shell


For Thursday’s Lecture:Read Chapter 26, sections 4-7

Complete Reading Self-Check 01B (Due Thurs 2 am)

Lab/Recitation this week: Only meets W/R - an exploration of electric field line diagrams - print from Angel & bring to class.

In Thursday’s Reading:

1. What do E fields of “common” shapes (rings, planes spheres, discs) look like? (And how are the E fields expressions derived?)

3. How do charges move in an E field? (Do they move along E field lines?)

2. What is a parallel plate capacitor and why is it useful for E fields?

4. How do dipoles behave in an E field?


In your reading for next class: For charge distributions calculations, you

want to come away knowing:

1. How the electric field formula was

derived (in textbook)

2. For infinite distributions, how do they depend on

distance (r)

3. For finite distributions, how do they behave in near & far limits

The formula itself is less important

- what was dq? - i.e., how did they turn dq into an integral over position?- how were vectors used?- how was symmetry used?

phys 212 lecture 03pre-electric fields

Documents

electric field vectors

electric field lines

source of field

fieldgravitational field

field idea

kind of field

charge field experienced

penn state univelectric