Vector Addition

The order in which A and B are added is not significant, so that A + B = B + A

To add vector B to vector A, draw B so that its tail is at the head of A. The vector sum A + B is the vector R that joins the tail of A and the head of B.

Usually, R is called the resultant of A and B.

Exactly the same procedure is followed when more than two vectors of the same kind are to be added. The vectors are strung together head to

The resultant R is the vector drawn from the tail of the first vector to the head of the last.

Pythagorean TheoremThe sum of the squares of the short sides of a right triangle is equal to the square of its hypotenuse. For the triangle of Figure on next slide

Hence, we can always express the length of any of the sides of a right triangle in terms of the lengths of the other sides:

The sum of the interior angles of any triangle is 180°. Since one of the angles in a right triangle is 90°, the sum of the other two must be 90°. ( + = 90°).

The three basic trigonometric functions the sine, cosine, and tangent of an angle are defined in terms of the right triangle of as follows:

The inverse of a trigonometric function is the angle whose function is given.

Q. A woman walks eastward for 5 km and then north-ward for 10 km. How far is she from her starting point? If she had walked directly to her destination, in what direction would she have headed?

Solution. R = A2 + B2

The length of the resultant vector R corresponds to a distance of 11.2 km, and a protractor shows that its direction is 27 east of north.

Q. Find the values of the sine, cosine, and tangent of angle in Figure.

Solution.

Electric Charge

Electric charge, like mass, is one of the basic properties of certain elementary particles of

which all matter is composed.

OR

Electric charge is an intrinsic characteristic of the fundamental particles making up those objects; that is , it is a property that comes automatically with those particles

wherever they exist.

The vast amount of charge in an every object is usually hidden because the object

contains equal amount of two kinds of charge: Positive

charge and negative charge.

The effects of electric charge were first observed as static

electricity:

The physics of electromagnetism was first studied by the early Greek Philosophers, who discovered that if a piece of amber is rubbed and

brought near bits of straw, the straw will jump to the amber.

The attraction between amber and straw is due to electric force.

After being rubbed on a piece of fur, an amber rod acquires a charge and can attract small objects.

So there are two types of Electric charges, positive charge and

negative charge

Electric ChargeCharging both amber and glass rods shows that there are two types of electric charge;

Electric charges of the same sign repel each other.

Opposite electric charges attract each other.

The positive charge in ordinary matters is carried by protons and the negative by

electrons.

The atom

• An atom is a fundamental unit of matter• made up of

• protons (with a positive charge)• neutrons (neutral – no charge)• electrons (with a negative charge)

The electrons in an atom are in a cloud surrounding the nucleus. Number of electrons and number of protons are equal, so the atom electrically is neutral.

Oxygen atom

What is electricity?•Everything is made of atoms which contain POSITIVE particles called PROTONS and NEGATIVE particles called ELECTRONS.

Proton (+)

Neutron

Electron (-)

•An atom will usually have the same number of positives and negatives•This makes the atom NEUTRAL.

Proton (+)

Neutron

Electron (-)

The Unit of charge is Coulomb (C).

All Electrons and Protons have exactly the same charge but different in sign.

The charge of the Proton is

+1.6 x 10-19 C

The charge of the Electron is

-1.6 x 10-19 C

Charge is Quantized When a physical quantity such as charge can have only discrete values rather than any values, we say that quantity is quantized.

All charges in nature occur in multiples of a certain elementary

charge, + e = + 1.6 x 10-19 C

Any positive or negative charge q that can be detected can be written as

q = ne, n = +1, +2, +3,….

Charge conservation

This is the principle that electric charge can neither be created nor destroyed. The net quantity of electric charge, the amount of positive charge minus the amount of negative charge in the universe, is always conserved.

Statement of the principle was by American scientist Benjamin Franklin in 1747.

Mathematically, we can state the law as a continuity equation:

Q(t) is the quantity of electric charge in a specific volume at time t, QIN is the amount of charge flowing into the volume between time t1 and t2, and QOUT is the amount of charge flowing out of the volume during the same time period.

When matter is created from energy, equal amount of negative and positive charge always come into being, and when matter is converted to energy, equal amount of positive and negative charge disappear.For example, When a electron annihilates a positron(antielectron), they produce two or more gamma ray photons,

e− + e+ → γ + γ

In this Feynman diagram, an electron and a positron annihilate, producing a photon (represented by the

blue sine wave) that becomes a quark-antiquark pair, after which the antiquark radiates a gluon

(represented by the green helix).

Coulomb’s LawThe force one charge exerts an other is given by Coulomb’s Law The magnitude of the electrostatic force of interaction between two point charges is directly proportional to the multiplication of the magnitudes of charges and inversely proportional to the square of the distance between them. If the two charges have the same sign, the electrostatic force between them is repulsive; if they have different sign, the force between them is attractive.

Coulomb's law can also be stated as a simple mathematical expression. F = K q1q2 r2

where k is Coulomb's constant, q1 and q2 are the signed magnitudes of the charges, r the distance between the charges.The constant is the permittivity of free space in C2 m−2 N−1

Electric Field

Electric field induced by a positive electric charge

(Outward arrows)

Electric field induced by a negative electric charge(Inward arrows)

An electric field is a region of space in which a charge would be acted upon by an electric

force.

An electric field may be produced by one or more charges, and it may be uniform or it may vary in magnitude and/ or direction from place to place

Electric field is a region of space in which a charge would be acted upon by an electric force. An electric field may be produced by one or more charges.

If a charge q at a certain point is acted on by the force F, the electric field E at that point is defined as the ratio between F and q:

The unit of E is the Newton per Coulomb (N/C) or, more commonly, the equivalent unit volt per meter (V/m).Or E = potential difference = V/m

distance

The potential difference V between two points in an electric field, is the amount of work needed to take a charge of 1 C from one of the points to the other.

The potential difference between two points in a uniform electric field E is equal to the product of E and the distance s between the points in a direction parallel to E: V = Es

Example: A pith ball has a charge of +10-12 C. (a) does it contain an excess or a deficiency of electrons

compared with its normal state of electrical neutrality?(b)How many electrons? Solution: (a) Since the pith is positively charged, so some

electrons are needed to balance the positive charge of its nuclear protons.

(b) The charge of an electron is e = 1.6 x 10-19 C, q (is given) = +10-12C Number of electrons = ?

We know q = neHence, number of electrons = q/e

= 10-12 C1.6x 10-19 C

n = 6.25 x 106 electrons

What is electricity?So electricity is…

movement of charge round a circuit.

We call this electric current.

Charge, Current & Time

• Electric current is given the symbol

I• Electric current is the movement of• negative charges (electrons) in a• circuit

Charge, Current & Time

• Current is the amount of charge flowing• per second and is given the unit

•Amps (A)

Charge, Current & Time

•If current is charge flowing per second then

t

QI

time in seconds (s)

Current in Amps (A)

Charge transferred in coulombs (C)

so a current of 1 A is 1 C of charge transferred in 1 s.

Charge, Current & Time

•This can be rearranged as

•or

ItQ

I

Qt

Problem: The potential difference between a certain thundercloud and the ground is 7 × 106 V. Find the energy dissipated when a charge of 50 C is transferred from the cloud to the ground in a lightningstroke.Solution. The energy is

CURRENTA flow of charge from one place to another.

An electric circuit is a closed path in which an electric current carries energy from a source (such as a battery or generator), to a load (such as a motor or a lamp)

Electric Current:

• The flow of electric charges.

Electric Current, I

I = q t

• Rate• Unit: Coulomb / sec = Ampere (A)• Andre Ampere (1775-1836)

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Conventional current has the direction that the (+) charges would have in the circuit.

current is always supposed to go from the positiveterminal of a battery to its negative terminal.

Conductors:A conductor is a substance through which charge can flow easily, and an insulator is one through which charge can flow only with great difficulty. Metals, many liquids, and plasmas (gases whose molecules are charged) are conductors; nonmetallic solids, certain liquids, and gases whose molecules are electrically neutral are insulators.

Ohm’s Law

Problem 12.1 A 120-V electric heater draws a current of 25 A. What is its resistance?Solution:

Resistance• Depends on type of material, size and

shape, temperature. R=ρ L A

L: length of the wireA: cross-sectional areaρ: resistivity (inherent to material)

where L is the length of the conductor, A is the cross-sectional area, and r (Greek letter rho), is the resistivity of the material of the conductor. In SI, the unit of resistivity is the ohmmeter. The resistivity of most materials vary with temperature. If R is the resistance of a conductor at a particular temperature, then the change in its resistance R when the temperature changes by T is approximately proportional to both R and T so that

Temperature Dependence of Resistance

• For metals: as temperature increases the resistance increases. At very low temperatures resistance can become zero: superconductivity.

• For semiconductors: the opposite occurs.

Q. One method of painting a metal panel uses electrostatic charges. A paint spray produces paint droplets, all of which are given a positive charge. The metal panel is given a negative, charge as shown below

a) State the effect that charges have on each other (i) like charges (ii) unlike charges

b) (i) Explain why the droplets spread out as they leave the nozzle. (ii) Explain why it is important that the metal panel has a negative charge.

(iii) State one advantage of using electrostatics in this way to paint the metal panel.

• Direct Current• DC• Provided by batteries

• Alternating Current

• AC• Provided by power

companies

Example:

• What charge flows through a cross sectional area of a wire in 10min, if the ammeter measures a current of 5mA?

• Answer: 3C

Resistance

• Resistance of an object to the flow of electrical current.

• R= V / I

• Resistance equals the ratio of voltage to current.

• Unit: Ohm (Ω)

Ohm’s Law (Georg Ohm, 1787-1854)

V = IR

• The voltage , V, across a resistor is proportional to the current, I, that flows through it.

• In general, resistance does not depend on the voltage.

Resistor

• An object that has a given resistance.

A Battery Provides Energy

Electric Circuit• The battery “pumps” positive charges from

low (-) to high (+) potential.

Resistors use up Energy

Electric Circuit• A resistor uses up energy.

• When the current goes through the resistor it goes to a lower potential.

Question:

Electric Circuit• Which point has a lower potential, A or B?

Example:

• Calculate the current through a 3 Ω resistor when a voltage of 12V is applied across it.

• Answer: 4 A

Example:

• A 6 Ω resistor has a power source of 20V across it. What will happen to the resistance if the voltage doubles?

Potentiometer• A variable resistance.

• Used for dimmers, fan speed controls, etc.

Potentiometer Symbol

Example:

• Calculate the current through a 3 Ω resistor when a voltage of 12V is applied across it.

Answer: 4 A

Voltmeter

• Measures the voltage between two points in an electric circuit.

• Must be connected in parallel.

A voltmeter is connected in parallel.

Ammeter• Measures electric current.

• Must be placed in series.