Elec mag2

Electricity and Magnetism Electric forces hold atoms and

molecules together. Electricity controls our thinking, feeling,

muscles and metabolic processes. Electricity and magnetism underpin much of our current technology (e.g. computers). Electricity and magnetism are linked on a fundamental level.

Electricity

“Electricity" came from the Greek words "elektor," for "beaming sun" and "elektron," both words describing amber.

Amber is fossilized tree sap millions of years old and has hardened as hard as a stone.

The History of Electricity

• Electric => electron = Greek word for amber.(640 – 546 BC)

• “Rub amber with wool, and it will pick up bits of wood, feathers, straw …”

Thales of Miletus


• About 1736, Charles Francois du Fay (1698-1739) learned that rubbing glass and rubbing resinous substances (e.g., amber) seemed to produce charges of different kinds. He found that two charges of the same kind repelled each other, while two of unlike kinds attracted. He suggested that electricity might exist as two distinctly different types, which he named “vitreous” and “resinous” electricity.


• William Watson (1715-1790) suggested in 1746 that electricity was one “fluid”. One of the two kind of electricity proposed by Du Fay could be an excess () of this fluid and the other a difficiency of it (). Flow from to could account for electrical discharge. Benjamin Franklin (1706-1790) adopted and popularized Watson's “one fluid” theory and chose vitreous electricity to be the positive type (thereby giving electrons a negative charge). Franklin’s great reputation won universal acceptance for this view.

Static electricity is the imbalance of positive and negative charges.

Like charges repel and unlike charges attract.

When you take off a wool hat, it rubs against your hair. Electrons move from your hair to the hat. Now each hair has the same positive charge. The hairs try to get as far from each other as possible. The farthest they can get is by standing up and away from the others.

Static Electricity

Clouds get their charges as water and ice particles move and interact. Smaller, positively charged particles rise to the top of the cloud and larger, negatively charged particles gather at the bottom. When the buildup of charge is great enough, the oppositely charged particles attract and discharge their energy as a bolt of lightning.

When we charge something with static electricity, no electrons are made or destroyed. No new protons appear or disappear. Electrons are just moved from one place to another. The net, or total, electric charge stays the same. This is called the principle of conservation of charge.

• Two atoms were walking down the street one day, when one of them exclaimed, "Oh, no I've lost an electron!"

• "Are you sure?" the other one asked.

• "Yes," replied the first one, "I'm positive."

Static Charge

1. How can I demonstrate static charge using an inflated balloon?

A. Pop it. The sound it makes is due to static charge.

B. Rub it on cloth, rug, or hair, then it will stick to a wall.

C. Rub it on a metal surface, then use it to pick up bits of paper.

D. Drop it and time its fall. If it falls slower than a rock, it is affected by static charge.

E. Let the air out slowly. It will be larger than its original size due to static charge.

Demonstrations of Electrostatics

• Balloon• Glass rod/silk• Plastic rod/fur• Electroscope• Van de Graaf Generator

Glass Rod/Plastic RodA glass rod rubbed with silk gets a positive charge.A plastic rod rubbed with fur gets a negative charge.Suspend a charged glass rod from a thread, and another charged glass rod repels it.A charged plastic rod, however, attracts it.This mysterious force is called the electric force.Many similar experiments of all kinds led Benjamin Franklin (around 1750) to the conclusion that there are two types of charge, which he called positive and negative.He also discovered that charge was not created by rubbing, but rather the charge is transferred from the rubbing material to the rubbed object, or vice versa.

Charging Experiments (1)

Observations:

1. No force is observed between un-rubbed rods.

2. Plastic rods rubbed with wool repel each other.

3. Glass rod rubbed with silk attracts plastic rod rubbed with wool.

4. At increased distance, forces are decreased.


More Observations:1. A (charged) plastic rod rubbed with

wool attracts small pieces of paper.2. A (charged) plastic rods rubbed with

wool is attracted to an un-rubbed (neutral) plastic rod.

3. A plastic rod rubbed with wood is attracted to the wool, repelled by the silk.

4. No charged (rubbed) object attracts both the charged plastic rod and the charged glass rod.


Even More Observations:1. The charge from a plastic rod rubbed

with wool can be transferred to a metal sphere.

2. After the transfer, the plastic rod does not attract paper.

3. A 2nd metal sphere connected by a metal rod acquires the rod’s charge.

4. A 2nd metal sphere connected by a plastic rod does not acquire the rod’s charge.

Electric Charges• Evidence for electric charges is everywhere, e.g.

– static electricity.– lightning.

• Objects may become charged by contact and frictional forces.

• Benjamin Franklin (1700’s) discovered that there are two types of charges:– positive charge.– negative charge.

• Franklin also discovered that like charges repel and unlike charges attract one another.

• Electric charge is– quantized (Millikan)– conserved (Franklin)

Electric Charges in Atoms• Atoms consist of a nucleus

containing positively charged protons.

• The nucleus of an atom is surrounded by an equal number of negatively charged electrons.

• The net charge on an atom is zero.

• An atom may gain or lose electrons, becoming an ion with a net negative or positive charge.

• Polar molecules have zero net charge but their charges are unevenly distributed in space (e.g. water).

Nuclear diameter ~ 10-15 m (femtometer)

Atomic diameter ~ 10-9 m (nanometer)

Electricity in Nature

• Most dramatic natural electrical phenomenon is lightning.

• Static electricity (balloons, comb & paper, shock from a door knob)

• Uses—photocopying, ink-jet printing

Insulators and Conductors (1)

If a conductor is charged, all of the charge must reside on the outer surface (and none in the interior.)

If an insulator is charged, the charge may (or may not) reside in the interior.

Insulators and Conductors (2)

In insulators, the electrons are tightly bound in the atoms and are not free to move around. When insulators are charged, e.g. by friction, patches of molecular ions are created on the surface, but these patches are immobile.

In solid metal conductors, the outer (valence) electrons of the atoms are only weakly bound and are free to move around in the solid. The conductor as a whole may be electrically neutral, but the electrons are rather like an electrically charged liquid, a “sea” of electrons within the material. Electrons are the “charge carriers”.

There are other forms of conduction (in ionic liquids, etc.) in which the charge carriers are not electrons.

Charging an Insulator

Charging a Conductor

Conductors cannot be charged by friction.

However, charge can be transferred to a conductor by contact with a charged object.

The charges arriving at the conductor stay on the outer surface and distribute themselves over that surface so that they are as far away as possible from the repulsive forces of the other charges.

The Electroscope

Charging an Electroscope

The angle of deflection of the leaves provides a rough indication of the amount of charge that has been deposited on the electroscope.

Discharging a Charged Object

The human body, composed mainly of salty water, is a moderately good conductor. Therefore, a person touching a charged object will normally discharge the object.

Where the charge goes next depends on the degree to which the person is insulated from ground (e.g., by rubber shoe soles).

Charge Polarization

Induced Charge

By using charge polarization, it is possible to induce charge on an electrically neutral object.

Example: Bring a charged rod near (but not touching) an electroscope and observe the effect on the leaves.

Charges and Forces

The Electric Dipole

• Experiment: Bring a positive charge near a neutral atom.

Classes of Materials• CONDUCTORS are materials in which

charges may move freely (e.g. copper).

• INSULATORS are materials in which charges cannot move freely (e.g. glass).

• SEMICONDUCTORS are materials in which charges may move under some conditions (e.g. silicon).

Charges and the Earth

• The earth acts as a near-infinite source or sink of charges, and therefore its net charge cannot easily be changed.

• Any conductor in contact with the earth is said to be GROUNDED and cannot receive a net charge. (principle of lightning rod)

Induced Charge• Charged objects brought close to a conductor may

cause charge to redistribute (polarize the conductor).

• If a polarized conductor is momentarily grounded, charge will be transferred to/from the earth, and it may be left with a net charge (by INDUCTION).

• Objects may be charged by– conduction (requires contact with another

charged object.– induction (requires no contact with another

charged object).

Electric Force and Coulomb’s Law• If two point charges q1 and q2 are separated

by a distance r, the magnitude of the electric force Fe between them is:

221

r

qqkFe

where k = 8.99 x 10 9 N m2/C2 is the Coulomb constant, q1 and q2 are in Coulombs (C), r is

in meters (m) and Fe is in Newtons (N).

Quantum of Electric Charge

• Electric charge is quantized. The smallest possible unit is the charge on one electron or one proton: e= 1.602 x 10-19 Coulombs

• No smaller charge has ever been detected in an experiment.

Electric Force Vector

• The force on a point charge q1 exerted by another point charge q2 separated by a distance r21 is:

. and joining

axis thealongr unit vecto a is ˆ where

ˆ

12

21

122121221

2112

qq

r

FFrr

qkqF

Principle of Superposition

• For a system of N charges q1, q2, q3, …, qN,

the resultant force F1 on q1 exerted by charges

q2, q3, …, qN is:

NFFFF 113121

• Each charge may be considered to exert a force on q1 that is independent of the other

charges present.

Field Forces and Electric Field

• Field forces act through space even if there is no contact (e.g. gravitational force).

• The ELECTRIC FIELD E is defined in terms of the electric force that would act on a positive test charge q0 :

N/Cin 0q

FE e

Electric Field• The electric force on a positive test charge q0

at a distance r from a single charge q:

rr

qqkFe ˆ

20

• The electric field at a distance r from a single charge q:

rr

qk

q

FE e ˆ

20

EqFe

0

Electric Field due to a Group of Charges:

ii i

i rr

qkE ˆ

2

0i tofromr unit vecto a is ˆ q qri

Example ProblemFour point charges are at

the corners of a square of side a as shown.

a) Determine the magnitude and direction of the electric field at the location of q.

b) What is the resultant force on q?

2q q

4q3q

a

a

a

a

Electric Field LinesElectric Field Lines:• describe the direction of the electric field at any point• The density of field lines is proportional to the

magnitude of the electric field.• The directions of arrows indicate the direction of the

force on a positive test charge.

• Rules:– Lines begin on + charge and end on – charge– Number of lines approaching or leaving a charge

is proportional to the magnitude of the charge.– Electric field lines may never cross.

Electric Field Lines: Conventions Positive Point Charge Negative Point Charge

Electric Field lines

Assignment # 3

1. A solid brass sphere 0f 5.00 mm radius on which there is a positive charge of 800 statC is put in contact with a hollow brass sphere of the same radius which is a negative charge of 500 statC . The spheres are then separated so that there is a distance of 200 mm between their centers. What is the force between them?

2. Calculate the position of the point charges in the neighbourhood of two point charges of 1.67 µC and -0.0600µC, situated 400mm apart where a third charge would experience no force.

3. Two small spheres having a mass of 300mg each and having equal charges are suspended from the same point by silk strings 100 cm long. When spheres are kept 15.o cm apart by electrostatic repulsion, what is the charge on each?

Assignment # 3

4. The sides of a right triangle are BC = 3, AC = 4, and AB = 5cm. If + 10 statC charges are placed, at the corners B and C, what is the magnitude and direction of the electric field intensity at A?

5. Two similar small conductors have charges of +25 and -10 statC, respectively. They are placed in contact and then separated until their centers are 8.0 cm apart. What is the force between them at this position?

6. Two small, charged metal spheres are placed 20 cm apart in air. If they have + 20, and -40 statC charges on them, respectively, what force acts on them? At what point between them would the electric field intensity be zero?

Elec mag2

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