Lecture 3: Chapter 19 Cont -...

transcript

Lecture 3: Chapter 19 Cont

Electric Charges, Forces and

Electric Fields

Agenda

Compare the electric force to Gravitational force

Superposition of forces

Electric Field

Superposition of Electric Field

Shielding and Charging by Induction

Electric Flux and Gauss’s Law

What did we study last lesson?

Electric Charges: positive and neg.

Electron (neg) and proton (pos)

Charges are conserved

Polarization

Insulators & Conductors

Coulomb’s Law

Two rods and a cat fur:

Glass Rod (positive charges)

Rubber Rod (negative)

Charging by Conduction

Coulomb’s Law

(electrostatic force between point charges)

Polarization is realignment of charge within individual molecules.

Produces induced charge on the surface of insulators.

how e.g. rubber or glass can be used to supply electrons.

Student Discussion

A positively charged object hanging from a string is brought near a non conducting object (ball). The ball is seen to be attracted to the object.

1.Explain why it is not possible to determine whether the object is negatively charged or neutral.

2.What additional experiment is needed to reveal the electrical charge state of the object?

Two possibilities:

Attraction between objects of unlike charges.

Attraction between a charged object and a neutral object subject to polarization.

+ - - - -

+ + + +

What additional experiment is needed to reveal the electrical charge state of the object?

Two Experiments:

Bring known neutral ball near the object and observe whether there is an attraction.

Bring a known negatively charge object near the first one. If there is an attraction, the object is neutral, and the attraction is achieved by polarization.

- + + + +

+- -+-

Question

Name the first action at a distance force you have encountered in physics so far.

Electric Force

Electrical Forces are Field Forces

This is the second example of a field force Gravity was the first

Remember, with a field force, the force is exerted by one object on another object even though there is no physical contact between them

There are some important similarities and differences between electrical and gravitational forces

Electrical Force Compared to Gravitational Force

Both are inverse square laws

The mathematical form of both laws is the same Masses replaced by charges

G replaced by ke

Electrical forces can be either attractive or repulsive

Gravitational forces are always attractive

Consider a proton (mp=1.67x10-27 kg; qp=+1.60x10-19 C) and an electron (me=9.11x10-31 kg; qe=-1.60x10-19 C) separated by 5.29x10-11 m. The particles are attracted to each other by both the force of gravity and by Coulomb’s law force. Which of these has the larger magnitude? A. Gravitational force B. Coulomb’s law force

Example: Student Participation

Which of these has the larger magnitude? A. Gravitational force B. Coulomb’s law force

N102.8

1029.5

1060.11060.11099.8 :Coulomb

N106.31029.5

1011.91067.11067.6 :Gravity

312711

We will mostly ignore gravitational effects when we

consider electrostatics.

The steps will be found on Pg. 659. By what factor the electric force is greater than the gravitational force?

Problem solving steps

1. Visualize problem – labeling variables

2. Determine which basic physical principle(s) apply

3. Write down the appropriate equations using the variables

defined in step 1.

4. Check whether you have the correct amount of

information to solve the problem (same number of

knowns and unknowns).

5. Solve the equations.

6. Check whether your answer makes sense (units, order of

magnitude, etc.).

Superposition Principle

From observations: one finds that whenever multiple charges are present, the net force on a given charge is the vector sum of all forces exerted by other charges.

Electric force obeys a superposition principle.

The Superposition Principle

How to work the problem?

Find the electrical forces between pairs of charges separately

Then add the vectors

Remember to add the forces as vectors

F12 F13

Superposition Principle Example: 3 charges in a line

q1 = 6.00 uC q2 = 1.50 uC q3 = -2.00 uC d1 = 3.00 cm d2 = 2.00 cm K = 8.99 x 109 N.m2 /C2

Example: Superposition Principle (Not along a line)

Consider three point charges at the corners of a triangle, as shown in the next slide. Find the resultant force on q3 if

q1 = 6.00 x 10-9 C

q2 = -2.00 x 10-9 C

q3 = 5.00 x 10-9 C

Superposition Principle Example

The force exerted by q1 on q3 is

The force exerted by q2 on q3 is

The total force exerted on q3 is the vector sum of

22 9/4/2013

Consider three point charges at the corners of a triangle, as shown below. Find the resultant force on q3.

Solution:

3 2 9 9

3 1 9 8

5.00 10 2.00 108.99 10 5.62 10

5.00 10 6.00 108.99 10 1.08 10

cos37.0 3.01 10

sin 37.0 6.50 10

7.16 10

C Cq qF k N

F F F N

Spherical Charge Distribution

Students need to read and work on pg 663/664

24 9/4/2013

Electric Field - Discovery

Electric forces act through space even in the absence of physical contact.

Suggests the notion of electrical field (first introduced by Michael Faraday (1791-1867).

Electric Field

A charged particle, with charge Q, produces an electric field in the region of space around it

A small test charge, qo, placed in the field, will experience a force.

“The electric field is the force per charge at a given location”

Electric Field

Mathematically,

SI units are N / C

Given: One finds:

q qF k

Electric Field

Use this for the magnitude of the field

The electric field is a vector quantity

The direction of the field is defined to be the direction of the electric force that would be exerted on a small positive test charge placed at that point

Direction of Electric Field

The electric field produced by a negative charge is directed toward the charge

A positive test charge would be attracted to the negative source charge

Direction of Electric Field, cont

The electric field produced by a positive charge is directed away from the charge

A positive test charge would be repelled from the positive source charge

Electric Field

More About a Test Charge and The Electric Field

The test charge is required to be a small charge

It can cause no rearrangement of the charges on the source charge

The electric field exists whether or not there is a test charge present

The Superposition Principle can be applied to the electric field if a group of charges is present

Electric Fields and Superposition Principle

The superposition principle holds when calculating the electric field due to a group of charges

Find the fields due to the individual charges

Add them as vectors

Use symmetry whenever possible to simplify the problem

Problem Solving Strategy, cont

Apply Coulomb’s Law

For each charge, find the force on the charge of interest

Determine the direction of the force

Sum all the x- and y- components

This gives the x- and y-components of the resultant force

Find the resultant force by using the Pythagorean theorem and trig

Examples of Electric Field

a) E will be constant (a charged plane)

b) E will decrease with distance as (a point charge)

c) E in a line charge, decrease with a distance 1/r

35 9/4/2013

Example:

An electron moving horizontally passes between two horizontal planes, the upper plane charged negatively, and the lower positively.

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

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

36 9/4/2013

Example:

A uniform, upward-directed electric field exists in this region. This field exerts a force on the electron. Describe the motion of the electron in this region.

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

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

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

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

Observations:

Horizontally:

No electric field

No force

No acceleration

Constant horizontal velocity

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

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

Observations:

Vertically:

Constant electric field

Constant force

Constant acceleration

Vertical velocity increase linearly with time.

y o o o

a q E m

v q E t m

y q E t m

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

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

Conclusions:

The charge will follow a parabolic path downward.

Motion similar to motion under gravitational field only except the downward acceleration is now larger.

Example: Electric Field Due to Two Point Charges (Superposition of Fields)

Question:

Charge q1=7.00 mC is at the origin, and charge q2=-10.00 mC is on the x axis, 0.300 m from the origin. Find the electric field at point P, which has coordinates (0,0.400) m.

0.300 m q1 q2

Question: Charge q1=7.00 mC is at the origin, and charge q2=-10.00 mC is on the x axis, 0.300 m from the origin. Find the electric field at point P, which has coordinates (0,0.400) m.

Observations: First find the Electric field at point P due to

charge q1 and q2.

Field E1 at P due to q1 is vertically upward.

Field E2 at due to q2 is directed towards q2.

The net field at point P is the vector sum of E1 and E2.

The magnitude is obtained with

Set up the problem:

q1=7.00 mC

q2=-10.00 mC

K = 8.99 x 109 N. m2 /C2

r1 = 0.400m

r2= ? What do we do?

1) Calculate r2

2) Calculate the electric field at P

3) I will set it up, but you will need to finish (it looks like example in pg. 669)

Solution:

Electric Field Lines

A convenient aid for visualizing electric field patterns is to draw lines pointing in the direction of the field vector at any point

These are called electric field lines and were introduced by Michael Faraday

Electric Field Line Patterns

Point charge

The lines radiate equally in all directions

For a positive source charge, the lines will radiate outward

For a negative source charge, the lines will point inward

An electric dipole consists of two equal and opposite charges

The high density of lines between the charges indicates the strong electric field in this region

Two equal but like point charges

At a great distance from the charges, the field would be approximately that of a single charge of 2q

The bulging out of the field lines between the charges indicates the repulsion between the charges

The low field lines between the charges indicates a weak field in this region

Electric Field Patterns

Unequal and unlike charges

Note that two lines leave the +2q charge for each line that terminates on -q

Rules for Drawing Electric Field Lines

The lines for a group of charges must begin on positive charges and end on negative charges In the case of an excess of charge, some

lines will begin or end infinitely far away

The number of lines drawn leaving a positive charge or ending on a negative charge is proportional to the magnitude of the charge

No two field lines can cross each other

Electric Field Lines, final

The electric field lines are not material objects

They are used only as a pictorial representation of the electric field at various locations

They generally do not represent the path of a charged particle released in the electric field

Question:

Is it safe to stay inside an automobile during a lightning storm? Why?

Mini-Discussion

54 9/4/2013

Question:

Is it safe to stay inside an automobile during a lightning storm? Why?

Answer:

Yes. It is. The metal body of the car carries the excess charges on its external surface. Occupants touching the inner surface are in no danger.

Shielding and Charging by Induction

When no net motion of charge occurs within a conductor, the conductor is said to be in electrostatic equilibrium

An isolated conductor has the following properties: The electric field is zero everywhere inside the

conducting material

Any excess charge on an isolated conductor resides entirely on its surface

Properties, cont

The electric field just outside a charged conductor is perpendicular to the conductor’s surface

On an irregularly shaped conductor, the charge accumulates at locations where the radius of curvature of the surface is smallest (that is, at sharp points)

Property 1

The electric field is zero everywhere inside the conducting material Consider if this were not true

If there were an electric field inside the conductor, the free charge there would move and there would be a flow of charge

If there were a movement of charge, the conductor would not be in equilibrium

Property 2

Any excess charge on an isolated conductor resides entirely on its surface

A direct result of the 1/r2 repulsion between like charges in Coulomb’s Law

If some excess of charge could be placed inside the conductor, the repulsive forces would push them as far apart as possible, causing them to migrate to the surface

Electric Flux

Field lines penetrating an area A perpendicular to the field

The product of EA is the flux, Φ

In general:

ΦE = E A cos θ

Electric Flux, cont.

ΦE = E A cos θ The perpendicular to the area A is at an

angle θ to the field

SI unit: N.m2 /C

If the surface is close, the sign is The flux is positive for field lines that leave

the enclosed volume of the surface

The flux is negative for field lines that enter the enclosed volume of the surface.

Gauss’ Law

Gauss’ Law states that the electric flux through any closed surface is equal to the net charge Q inside the surface divided by εo

εo is the permittivity of free space and equals 8.85 x 10-12 C2/Nm2

The area in Φ is an imaginary surface, a Gaussian surface (spherical surface) (derivation in pg. 676)

insideE

SI unit;

N.m2 /C

Electric Field of a Charged Thin Spherical Shell

The calculation of the field outside the shell is identical to that of a point charge

The electric field inside the shell is zero

Electric Field of a Nonconducting Plane Sheet of Charge

Use a cylindrical Gaussian surface

The flux through the ends is EA, there is no field through the curved part of the surface

The total charge is Q = σA

Note, the field is uniform

Electric Field of a Nonconducting

Plane Sheet of Charge, cont.

The field must be perpendicular to the sheet

The field is directed either toward or away from the sheet

Parallel Plate Capacitor

The device consists of plates of positive and negative charge

The total electric field between the plates is given by

The field outside the plates is zero

What did we study?

Electric Force (Coulomb’s force): Superposition of forces

l Electric Field (point charge):

Definition of electric Flux, :

Gass’s Law electric Flux (q is enclosed by a surface):

ΦE = E A cos θ

insideE

Lecture 3: Chapter 19 Cont -...

Documents