Electricity and magnetism around the house

• What do we know about electricity for devices that use batteries? Physical quantities? Units?

• What everyday knowledge to we have about electricity from our house outlets? Quantities? Units? Devices?

• When and where do we encounter electricity in nature? Quantities? Units?

• What permanent magnetic devices do we have around the house? Quantities? Units? [Also, magnetism in nature?]

• What devices use magnets that change with time?

• What devices use electromagnetism? Physical quantities? Units?

• And finally, what about Ohms?

OH

Benjamin Franklin, 1706-1790as inventor and scientist

stove, bifocals, swim fins, glass harmonica, libraries, fire departments, lightning rod

positive and negative charge, general idea of current flow,

lightning experiment

introduced terminology: “battery, conductor, condenser, charge, discharge, uncharged,

negative, minus, plus, electric shock, electrician”

The experimental beginnings…

Experiment by Philip Kreider et al (U of A) in 1980’s: model rocket with wire is used to trigger lightning.

Benjamin Franklin got very lucky that his kite only “tickled the tail of the dragon”.

How is the force affected by the signs of the

charges?

Experiments also showed that energy is conservedby this force. From our knowledge of dynamics,

how would we classify this force? If the charges were attached to free masses, what could we say about their possible motions?

Later experiments showed in detail how the force between two charges acts.

Pith ball demo.

Charles-Augustin de Coulomb1736-1806

contributions to mechanics: friction and viscosity

1777, invented the torsion balanceto measure the electric force between two charges, determining how the force varies

with distance:

Coulomb’s Law

Coulomb’s Torsion Balance

The fiber twists elastically, so that the force is proportional to the angle. After calibration, the

force and distance between spheres can be read from the scales.

Think a bit about how the measurement is done, since the force twists the fiber…

Coulomb could also vary the charges in a controlled way! More later…

OH

Coulomb’s Law

221

rqkqF =

229229 /CNm 100.9~/CNm 10988.8 ××=k

Force betweencharges.

Units: Newtons (N)

Charges 1 and 2.Units: Coulombs (C)

Distance between the two charges, squared.

k is the constant that sets the strength of F.

OH graph force

• Example: Two small objects have charges of +1.0 C and -1.0 C, and are separated by a distance of 1.0 m. What is the force between them? Large!

OH

This example shows us that in many practical situations we should use smaller units. For example, for charge:

CfCmbfemtocouloCpCbpicocoulomCnCbnanocoulomCCmbmicrocouloCmCmbmillicoulo

15

12

9

6

3

10 10 10 10 10

−

−

−

−

−

μ

For some quantities we introduce later we will be needing larger units. So it would be a good time to review all the prefixes now:

k, M, G, T, P, …

In case you need more orders of

magnitude…

Quarks & leptons are smaller than this.

PETA

TERA

Now we will spend a little time looking at the behavior of charges at the atomic level.

Why? To better understand the behavior of electricity in the macro-scale objects we

deal with every day.

“Why” does the force vary as the inverse square of r ?

221

rqkqF =

The answer is not simple. It depends on quantum mechanics, and quantum field theory. But just knowing a couple of facts will help us understand the electric force from a modern viewpoint:

(1)Visible light, and other electromagnetic waves, are composed of particles (or “quanta”) known as photons. (Photons are massless.)

(2)Photons are also the carriers of the electric force. For example, charged particles in an atom are continuously exchanging photons back and forth. This effect is not classical, since it leads to both attraction and repulsion.

With (2) in mind, consider how the intensity of light from the sun changes as you move further from the sun. This is not a rigorous proof, but it gives you the general idea of how the inverse square of r comes about.

OH discuss sphere

Robert A Millikan1868-1953

In 1909, Millikan showed, in his famous “oil drop experiment” at the University of Chicago, that charge is packaged (quantized) in units of “e”:

The charged building blocks of atoms, electrons and protons, are equally

and oppositely charged in these units:

electron: q = - eproton: q = + e

Ce 191060.1 −×=

Electric forces inside atoms: a delicate balance

• Opposite charges attract:Electrons (-) are held in their orbits by the electric force attracting them to protons in the nucleus (+).

• Like charges repel: The protons in the nucleus would like to fly apart! They are held together by the nuclear force, which is stronger than the electric force. The electrons also repel each other.

• Atoms are neutral: The positive and negative charges are equal in number.

Ions: atoms with unbalanced charge

• Positive ions are atoms with too few electrons to cancel the positive charges in the nucleus.

• Negative ions have one or more “extra” electrons, and have net negative charge.

Putting things into motion…

Example: In a hydrogen atom, the electron has a charge -e and the proton, +e. Their average distance of separation is 5.3 x 10-11 m. What is the force between them?

OH

Now we return to consideration of macro-scale objects and the behavior of electric

charges in their interiors and on their surfaces.

How do objects acquire a charge +q or –q ?Explain at the atomic level.

Insulators and conductors

• Insulators: Inner electrons are bound to their “own” atoms. Outer (valence) electrons are trapped in the bonds between atoms, and cannot move freely within the material.

• Conductors: All valence electrons are shared among all the bonds between atoms in the metal. They can be pictured as a “sea”, or “gas” of electrons, which are free to move.

Charging a conductor by contact

Once the flow of charge has stopped, the excess charge on any conductorresides on its surface: basically, due to repulsion (more later). In this example, electrons have been added, charging the conductor negative.

Charging an insulator

The charge distribution on an insulator is “anything you can create” by adding or removing electrons. In this example, electrons have been added uniformly throughout the insulator. But they could have been “painted” on the surface by contact charging.

Polarizing a conductor

What happens if the rod is negatively charged? Again,

what is the net force?

What is the net force on the conductor?

Polarizing an insulator

As in the case of the conductor, the near surface has excess negative charge, and the far surface, excess positive. (Again, consider case of opposite external charge…)

The atoms are individually polarized, but the electrons have not moved far from their original positions. So in most cases the induced surface charge is much weaker than for a conductor. Different insulators have different “polarizabilities”.

If the external charge is positive, what is the

net force on the conductor?

Charging objects by friction: “triboelectricity”

Method

Result

Electroscopes: devices to measure electric charge

Gold Leaf Deflection Arm

Charging an electroscope by contact

Polarizing an electroscope(no contact)

Charging an object by induction

Charging an electroscope by induction

Now look at the electroscope with both plastic (-) and glass (+) rods:

Charge by contact and study the behavior of the electroscope for different charge sign combinations when the rods are:

(1) brought nearby (2) brought into contact.

Charge by induction and verify the previous picture by checking charge signs.

Electric force vectors from different charges add. This is called the “superposition principle”.

At the fundamental level, this happens because virtual photons carrying the force between charges are neutral, and do not interact with each other.

ii i

i

iiQQ r

rkQqFF ˆ2∑∑ ==

rr

+

+

+

+

Q

q3

q2

q1

Consider flipping some charge signs. Recall how we add vectors graphically.

r1

r3

r2

F

Vector addition graphically (for sketches).

Adding two vectors by parallelogram method

Adding two or more vectors successively V = V1 + V2 + …

V

V2

V1

V = V1 + V2

V

V2

V1

V

V2V1

Force problems in one dimension

Can the forces on q3 be balanced? Is this always possible?

Forces in basic charge configurations

Consider the possibilities for this case as well. (See next slide for one example.)

Typical force problem involving vector addition.

Problem: Find the net force on q3.We must use vector addition, just as we did to solve many classical mechanics problems. Start by making a careful sketch, then:

•Find magnitude of each force on q3 due to other q’s, using Coulomb’s Law:

Fi3 = kqiq3/ri32.

•Find angles from the given geometry.

•Sum x components to find F3x-net, then repeat for F3y-net. From these find the magnitude and direction of F3. Compare to sketch!

Set up and analyze this symbolically.

a

b

Electric dipole and forces on a third charge

+Q

-Q

+q

x

yDipole charges are equal and opposite, and equal distances from the x axis.

Sketch force field.

r+

r-

Two positive charges and a acting on a third charge.

The two q’s are not called a “dipole” unless they are equal

and opposite.