SPH4U

Electric ForcesMr. Burns

Maxwell’s Equations

0

E

0B

BE

t

0 0 0

EB u J

t

Gauss’s Law: The electric field’s mapping is equal to the charge density divided by the permittivity of free space. The relationship between electric field and electric charge

Gauss’s Law for Magnetism: The net magnetic flux out of any closed surface is zero. There is no such thing as a magnetic monopole

We can make an electric field by changing a magnetic field

We can make a magnetic field with a changing electric field or with a current

0 0

1c

0

E

Maxwell’s 1st Equation.

Maxwell’s first equation is Gauss’s Law. This equation tells us that electric field lines (E) DIVERGE outward from positive charges and CONVERGE inward to the negative charges.

Maxwell’s 2nd Equation.

Maxwell’s second equation tells us that the magnetic field (B) never DIVERGES or CONVERGE. They always go around in closed loops, therefore there doesn’t exist a single magnetic pole.

0B

Maxwell’s 3rd Equation.

Maxwell’s third equation is Faraday’s Law. This equation tells us that electric field lines (E) CURL around changing magnetic fields (B) and that changing magnetic fields induce electric fields.

BE

t

Maxwell’s 4th Equation.

Maxwell’s fourth equation tells us that the magnetic field (B) lines CURL around electric currents AND that magnetic field (B) lines CURL around changing electric fields.

0 0 0

EB u J

t

The Origin of Electricity

The electrical nature of matter is inherentin atomic structure.

kg10673.1 27pm

kg10675.1 27nm

kg1011.9 31em

C1060.1 19e

coulombs

The Origin of Electricity

In nature, atoms are normallyfound with equal numbers of protonsand electrons, so they are electricallyneutral.

By adding or removing electronsfrom matter it will acquire a netelectric charge with magnitude equalto e times the number of electronsadded or removed, N.

Neq

The Origin of Electricity

Example 1 A Lot of Electrons

How many electrons are there in one coulomb of negative charge?

Neq

1819-

1025.6C101.60

C 00.1

e

qN

Charged Objects and the Electric Force

It is possible to transfer electric charge from one object to another.

The body that loses electrons has an excess of positive charge, whilethe body that gains electrons has an excess of negative charge.

Charged Objects and the Electric Force

LAW OF CONSERVATION OF ELECTRIC CHARGE

During any process, the net electric charge of an isolated system remainsconstant (is conserved).

Charged Objects and the Electric Force

Like charges repel and unlike charges attract each other.

Lightning

Conductors and Insulators

Not only can electric charge exist on an object, but it can also movethrough an object.

Substances that readily conduct electric charge are called electricalconductors.

Materials that conduct electric charge poorly are called electricalinsulators.

Charging by Contact and by Induction

Charging by contact.

Charging by Contact and by Induction

Charging by induction.

Charging by Contact and by Induction

The negatively charged rod induces a slight positive surface chargeon the plastic.

Physicists did not like the concept of “action at a distance” i.e. a force that was “caused” by an object a long distance away

They preferred to think of an object producing a “field” and other objects interacting with that field

Thus rather than ...

+

-

they liked to think...

+

-

Coulomb’s Law

Coulomb’s Law

Coulomb’s Law

COULOMB’S LAW

The magnitude of the electrostatic force exerted by one point chargeon another point charge is directly proportional to the magnitude of the charges and inversely proportional to the square of the distance betweenthem.

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r

qqkF

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Coulomb’s Law

Example 3 A Model of the Hydrogen Atom

In the Bohr model of the hydrogen atom, the electron is in orbit about thenuclear proton at a radius of 5.29x10-11m. Determine the speed of the electron, assuming the orbit to be circular.

221

r

qqkF

Coulomb’s Law

N1022.8

m1029.5

C1060.1CmN1099.8 8211

219229

2

21

r

qqkF

rmvmaF c2

sm1018.2

kg109.11

m1029.5N1022.8 631-

118

mFrv

Electrostatics Gravitational Force

Two types of charges (q): positive and negative

One type of mass (m): positive mass

Attraction (unlike charges) and repulsion (like charges)

Attraction (all masses)

F: F:

Potential energy: Potential energy:

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C/mN1099.8k

r

qqkF

2211

221

kg/mN1067.6G

r

mmGF

r

mmGPE 21

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qqkPE 21

Coulomb’s Law

Gravitational vs. Electrical Force

r

F Fq1

m1

q2

m2

* smallest charge seen in nature!

For an electron:

* q = 1.6 ´ 10-19 Cm = 9.1 ´ 10-31 kg

FF

elec

grav

= ´ +417 10 42.

Coulomb’s Law

1 22elec

q qF k

r

1 22grav

mmF G

r

1 2

1 2

elec

grav

F q q k

F m m G211

26.67 10

N mG

kg

29

28.99 10

N mk

C

Suppose your friend can push their arms apart with a force of 450 N. How much charge can they hold outstretched?

+Q -Q

2mF= 450 N

9

F 450Q r 2

k 9 10

= 4.47•10-4 C

-4 1519

12.8 10

1.6 14.47 10

0

ee

C

3115 9.1 10 kg

2.8 10 ee

152.54 10 kg

That’s smaller than one cell in your body!

2

2

kQF

r

Coulomb’s Law

Coulomb’s Law

Example 4 Three Charges on a Line

Determine the magnitude and direction of the net force on q1.

Coulomb’s Law

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231

13

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Coulomb’s Law

Find the net force exerted on the point charge q2. F32

F12

F42

2d

F32 F12

F42

y

xF net

423212net FFFF

Coulomb’s Law

Coulomb’s Law

The Electric Field

The positive charge experiences a force which is the vector sum of the forces exerted by the charges on the rod and the two spheres.

This test charge should have a small magnitude so it doesn’t affect the other charge.

The Electric Field

Example 6 A Test Charge

The positive test charge has a magnitude of 3.0x10-8C and experiences a force of 6.0x10-8N.

(a) Find the force per coulomb that the test chargeexperiences.

(b) Predict the force that a charge of +12x10-8Cwould experience if it replaced the test charge.

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N100.68

8

oq

F(a)

(b) N1024C100.12CN0.2 88 F

The Electric Field

DEFINITION OF ELECTRIC FIELD

The electric field that exists at a point is the electrostatic force experiencedby a small test charge placed at that point divided by the charge itself:

oq

F

SI Units of Electric Field: newton per coulomb (N/C)

The strength of the electric field can be

thought of as the ratio of the force on that charge and the test

charge itself

The Electric Field

It is the surrounding charges that create the electric field at a given point.

The Electric Field

Electric fields from different sourcesadd as vectors.

The Electric Field

Example 10 The Electric Field of a Point Charge

The isolated point charge of q=+15μC isin a vacuum. The test charge is 0.20m to the right and has a charge qo=+0.8μC.

Determine the electric field at point P.

oq

FE

2

21

r

qqkF

The Electric Field

2

9 2 2 6 6

2

8.99 10 N m C 15 10 C 0.80 10 C2.7N

0.20m

oq qF k

r

CN104.3C100.80

N 7.2 66-

oq

FE

The Electric Field

2r

qkE

The electric field does not depend on the test charge.

o

o

o qr

qqk

q

FE

12

Point charge q:

The Electric Field

Example 11 The Electric Fields from Separate Charges May Cancel

Two positive point charges, q1=+16μC and q2=+4.0μC are separated in avacuum by a distance of 3.0m. Find the spot on the line between the chargeswhere the net electric field is zero.

2r

qkE

The Electric Field

2

6

2

6

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dk

dk

21 EE 2r

qkE

2 24.0 3.0m d d

m 0.2d

The Electric Field

Conceptual Example 12 Symmetry and the Electric Field

Point charges are fixes to the corners of a rectangle in twodifferent ways. The charges have the same magnitudesbut different signs.

Consider the net electric field at the center of the rectanglein each case. Which field is stronger?

The Electric Field

THE PARALLEL PLATE CAPACITOR

Parallel platecapacitor

o o

q VE

A d

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charge density

Change in potential (voltage)

Distance between plates

Electric Field Lines

Electric field lines or lines of force provide a map of the electric fieldin the space surrounding electric charges.

Electric Field Lines

Electric field lines are always directed away from positive charges andtoward negative charges.

Electric Field Lines

Electric field lines always begin on a positive chargeand end on a negative charge and do not stop in midspace.

Electric Field Lines

The number of lines leaving a positive charge or entering a negative charge is proportional to the magnitude of the charge.

Electric Field Lines

Electric Field Lines

Conceptual Example 13 Drawing ElectricField Lines

There are three things wrong with part (a) of the drawing. What are they?

The Electric Field Inside a Conductor: Shielding

At equilibrium under electrostatic conditions, any excess charge resides on the surface of a conductor.

At equilibrium under electrostatic conditions, theelectric field is zero at any point within a conductingmaterial.

The conductor shields any charge within it from electric fields created outside the conductor.

The Electric Field Inside a Conductor: Shielding

The electric field just outside the surface of a conductor is perpendicular to the surface at equilibrium under electrostatic conditions.

Flash – Coulombs Law

Flash – Electric Forces