My Chapter 16 Lecture Outline

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MyChapter 16

LectureOutline

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Chapter 16: Electric Forces and Fields

•Electric Charge

•Conductors & Insulators

•Coulomb’s Law

•Electric Field

•Motion of a Point Charge in a Uniform E-field

•Conductors in Electrostatic Equilibrium

•Gauss’s Law (not taught !!)

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§16.1 Electric Charge

There are two kinds of electric charge: positive and negative.

A body is electrically neutral if the sum of all the charges in a body is zero.

Charge is a conserved quantity.

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The elementary unit of charge is e = 1.60210-19 C.

The charge on the electron is 1e.

The charge on the proton is +1e.

The charge on the neutron is 0e.

Experiments show that likes charges will repel each other and unlike charges will attract each other and that the force decreases with increasing distance between charges.

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An object can become polarized if the charges within it can be separated. When grounded, the sphere will be charged by induction.

+++

+

+

This body is electrically neutral.

By holding a charged rod near the body, it can be polarized.

+ ++

+

+

+++++

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Example (text problem 16.4): A metallic sphere has a charge of +4.0 nC. A negatively charged rod has a charge of 6.0 nC. When the rod touches the sphere, 8.2109 electrons are transferred. What are the charges of the sphere and the rod now?

Each electron has a charge 1.60210-19 C so the total charge transferred is 1.3 nC.

The rod is left with 6.0 nC + 1.3 nC = 4.7 nC of charge and the sphere now has +4.0 nC 1.3 nC = +2.7 nC of charge.

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§16.2 Conductors and Insulators

A conductor is made of material that allows electric charge to move through it easily.

An insulator is made of material that does not allow electric charge to move through it easily.

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§16.3 Coulomb’s Law

2

21

r

qqkF =

The magnitude of the force between two point charges is:

where q1 and q2 are the charges, r is the separation between the two charges and k = 8.99109 Nm2/C2.

22120

0

/NmC 1085.8 and 4

1 where −×== ε

πεk

and ε0 is called the permittivity of free space.

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r

q1 q2F21 F12

r

q1 q2F21 F12

The electric force is directed between the centers of the two point charges.

The electric force is an example of a long-range or field force, just like the force of gravity.

Attractive force between q1 and q2.

Repulsive force between q1 and q2.

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Example: What is the net force on the charge q1 due to the other two charges? q1 = +1.2 C, q2 = 0.60 C, and q3 = +0.20 C.

The net force on q1 is Fnet = F21 + F31

F31

F21

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The magnitudes of the forces are:

Example continued:

( )

N 108.3

m) 5.0(m) 2.1(

)C 1060.0)(C 102.1(/CNm 109

3

22

66229

221

2121

−

−−

×=

+

×××==

r

qqkF

( )

N 105.1

m) 2.1(

)C 1020.0)(C 102.1(/CNm 109

3

2

66229

231

3131

−

−−

×=

×××==

r

qqkF

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Example continued:

The components of the net force are:

N 100.2cos 32131,21,31,net

−×=+−=+= FFFFF xxx

N 104.1sin0 321,21,31,net

−×=+=+= FFFF yyy

Where from the figure38.0

m 1.3

m 5.0sin

92.0m 1.3

m 2.1cos

==

==

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Example continued:

The magnitude of the net force is:

N 104.2 32,net

2,netnet

−×=+= yx FFF

°=

==

35

70.0tan,net

,net

φ

φx

y

F

F

The direction of the net force is:

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§16.4 The Electric Field

gF mg =Recall :

EF qe =

Where g is the strength of the gravitational field.

Similarly for electric forces we can define the strength of the electric field E.

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2e

r

Qk

q

FE ==

For a point charge of charge Q, the magnitude of the force per unit charge at a distance r (the electric field) is:

The electric field at a point in space is found by adding all of the electric fields present.

∑=i

iEEnetBe careful! The electric field is a vector!

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Example: Find the electric field at the point P.

E is a vector. What is its direction?

Place a positive test charge at the point of interest. The direction of the electric field at the location of the test charge is the same as the direction of the force on the test charge.

q1 = +e

x = 0 m

q2 = 2e

x = 1 m

P

x = 2 m

x

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Locate the positive test charge here.

Direction of E due to charge 2

Direction of E due to charge 1

q1 = +e q2 = 2e

Px

Example continued:

P

q1 = +e q2 = 2e

x

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The net electric field at point P is: 21net EEE +=

The magnitude of the electric field is: 21net EEE −=

Example continued:

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Example continued:

( )N/C 106.3

m) 2(

)C 106.1(/CNm 109 102

19229

2

11

−−

×=××

==r

qkE

( )N/C 109.2

m) 1(

)C 106.1*2(/CNm 109 92

19229

2

22

−−

×=××

==r

qkE

N/C 105.2 921net

−×−=−= EEE

The net E-field is directed to the left.

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Electric field lines

Electric field lines are a useful way to indicate what the magnitude and direction of an electric field is in space.

Rules:

1. The direction of the E-field is tangent to the field lines at every point in space.

2. The field is strong where there are many field lines and weak where there are few lines.

3. The field lines start on + charges and end on charges.

4. Field lines do not cross.

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Pictorial representation of the rules on the previous slide:

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§16.5 Motion of a Point Charge in a Uniform E-Field

A region of space with a uniform electric field containing a particle of charge q (q > 0) and mass m.

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FBD for the charge q

Em

qa

maqEF

maFF

e

ex

=

==

==∑Apply Newton’s 2nd Law and solve for the acceleration.

Fe

x

y

One could now use the kinematic equations to solve for distance traveled in a time interval, the velocity at the end of a time interval, etc.

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Example: What electric field strength is needed to keep an electron suspended in the air?

FBD for the electron:

x

y

Fe

w

To get an upward force on the electron, the electric field must be directed toward the Earth.

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Apply Newton’s 2nd Law:

N/C 106.5

0

11−×==

===

=−=∑

emg

E

mgeEqEwF

wFF

e

ey

Example continued:

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§16.6 Conductors in Electrostatic Equilibrium

Conductors are easily polarized. These materials have free electrons that are free to move around inside the material.

Any charges that are placed on a conductor will arrange themselves in a stable distribution. This stable situation is called electrostatic equilibrium.

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When a conductor is in electrostatic equilibrium, the E-field inside it is zero.

Any net charge must reside on the surface of a conductor in electrostatic equilibrium.

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Just outside the surface of a conductor in electrostatic equilibrium the electric field must be perpendicular to the surface.

If this were not true, then any surface charge would have a net force acting on it, and the conductor would not be in electrostatic equilibrium.

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Any excess charge on the surface of a conductor will accumulate where the surface is highly curved (i.e. a sharp point).

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Summary

You need to remember:

•Properties of Conductors/Insulators

•Charge Induction

•Coulomb’s Law

•The Electric Field

•Motion of a Point Charge in an Electric Field