ELECTRICITY

 

 

Fundamental Laws of Electric Charges:

 

Opposite electric charges attract each other.

Similar electric charges repel each other.

Charged objects attract neutral objects.

Two neutral objects do not attract.

 

An object without charge is said to be neutral.

Atom has neutrons and proton in its nucleus, and electrons move around the nucleus.

Proton and neutrons do not move, but electrons can move in or out of the atoms.

If an atom has an excess of electrons, it is negatively charged.

If an atom has a deficit of electrons, it is positively charged.

 

 

Charging an Object:

 

Charging by friction

Charging by contact

Charging by Induction

 

 

Electrostatics and Electric Fields 

 

Gravitational force, magnetic force and electrostatic force act at a distance.

 

Protons:  positively charged, 1.60 x 10-19 C

Electrons: negatively charged, - 1.60 x 10-19 C

Neutrons: no electric charge, 0

 

Masses of Atomic Particles

Proton:  1.67x10-27 kg

Neutron:  1.67x10-27 kg

Electron:  9.11x10-31 kg

 

Law of Electric charges:

Opposite charges attract each other

Like charges repel each other

Charged objects attract some neutral objects

 

Protons donít move from the atomís nucleus, but electrons come or go.

 

Negative charge: excess electrons

Positive charge:  deficit of electrons

Neutral:  equal number of protons and electrons

 

Objects are charged in three general ways:  by friction, by contact, and by induction.

 

After rubbed two objects together, friction causes electrons flow from low affinity (eg: wool) to high affinity (eg: rubber).

 

Conductor:  electrons bound loosely, so electrons can easily be transferred (eg: metal)

Insulator:  Electrons bound tightly, so they can not be transferred easily.

 

 

Coulombís Law:

 

One coulomb (C) is the charge created by the excess or deficit of 6.24x1018 electrons.

Elementary charge (e):  charge created by the excess or deficit of only one electron.

 

The amount of charge one electron: 1 e- = 1.602 x 10-19 C

 

1 C = 6.24 x 1018 elementary charges

 

q = N e

 

q:  Quantity of charge on an object (C)

N:  number of electron

e:  Elementary charge (C)

 

q1 (+) and q (+) charges repels each other creating positive (+) repulsion force

q1 (-) and q (-) charges repels each other creating positive (+) repulsion force

q1 (+) and q (-) charges repels each other creating positive (-) attraction force

q1 (-) and q (+) charges repels each other creating positive (-) attraction force

 

Electric Fields:

 

By convention, test charge is selected as positive.

Field lines represent of the path of test charges.

Lines of similar potential are called equipotential lines.

Equipotential lines and field lines are perpendicular to each other.

 

 

Column Law versus the Law of Universal gravitation:
 

Electric field formula: Gravitational field formula:

ELECTRIC FORCE:

 

Fe Electric force (N).  It can either attract or repel.

If Fe is positive, it represents a repulsion.

If Fe is negative, it represents an attraction between two opposite charges.

Forces act along the line joining the two centres of the masses.

For more accurate results r should be longer and radius of the spheres should be smaller.

k: Coulombís constant
(k= 9x109 N.m2/C2
)

q1 and q2 :  Magnitude of charges in coulombs (C)

r:  Distance between the centers of the objects (m)
GRAVITATIONAL FORCE:

 

FG:  Magnitude of the force of gravity (N)

The force of gravity
is always attractive force.

M:  Mass of the central body (kg), example:  Earth

m: mass of an object around the central body (kg )

G:  universal gravitation constant
(G = 6.67 x 10-11 N.m2/kg2)

rDistance between the centres of two bodies (m)

ELECTRIC FIELD STRENGTH:

 

:  Electric field strength:  Electric force per unit positive charge  (N/C).  It is a vector quantity.

Fe:  Electric Force (N)

qt:  Magnitude of the test charge (test charge is positive )(C)

qm:  Magnitude of the point charge (C)

GRAVITATIONAL FIELD STRENGTH:

 

 


:  gravitational field strength (N/kg):  Gravitational force applied per unit body around the central body.  It is a vector quantity.

 
 

M:  Mass of the central body (kg), example:  Earth
ELECTRIC POTENTIAL ENERGY:

 

 

Ee:  Electric potential energy (Joules, J)

 

If q1 and q2 are opposite charges, Ee will be negative, and charges attract.

 

If q1 and q2 are similar charges, Ee will be positive, and charges repel.

 

GRAVITATIONAL POTENTIAL ENERGY:

 

 
 

EG:  Gravitational potential Energy (Joules, J).  It is always negative, when r approaches infinity.

ELECTRIC POTENTIAL:

Amount of work necessary to move a unit positive test charge from rest at infinity to rest at any specific point.

 

                       

 

 

Electric Potential (V):  Electric potential energy per unit positive charge (J/C)

 

V:  Electric potential (Volt, V) (J/C)

 

Ee:  Electric potential energy (Joules, J)


qt:  Magnitude of the test charge (C)

GRAVITATIONAL POTENTIAL:

 

Gravitational potential energy per unit mass of the object around the central body (J/kg)

EG / m = - G.M / r

ELECTRIC POTENTIAL DIFFERENCE (∆V):


 

It is the change in electrical potential when a charge is moved between two points in an electric field.  Potential difference is determined by measuring work done in moving a coulomb of change between two points.  Electric potential decreases in the direction of electric field.  It means positive test charge moves from higher potential to lower potential.


 

GRAVITATIONAL POTENTIAL DIFFERENCE:

Difference in the gravitational potential energy per unit mass of the object between two locations (J/kg)

ΔEe = Ee1 - Ee2

THE ELECTRON VOLT (eV):

The energy of one electron after it has been accelerated through a potential difference of one volt

Ee = q. ΔV

q = 1 e- = 1.602 x 10-19 C (charge in one electron)

V = 1 V

1 eV = (1.602x10-19 C) x (1 V)

1eV = 1.602x10-19 J
 

 

 

Energy:

Total energy of the two charges remains constant even though the distance between them changes.

ET = EE + EK

EE + EK = EE1 + EK1

 

W:  Work (difference in electric potential energy, Joules)

d:  distance (m)

 

W12 = Ee2 - Ee1

W12 = Fe (d2 Ė d1)

W12 =   qε(d2 Ė d1)

 

Work is the dot product of force and displacement

 

 

W:  Electric potential energy (Joules, J)

θ:  The angle between direction of force and direction of displacement

 

 

ELECTRIC FIELD STRENGTH BETWEEN TWO PARALLEL PLATES

 

Electric filed, electric force and acceleration are constant in the space between the parallel plates.

 

 

 

 

ε:   Electric filed strength (N/C).  Electric field is uniform (constant in magnitude and direction) in the space between the parallel plates.  Electric filed depends only on the magnitudes of the charges on the plates.

 

Example:

The electric field intensity between two parallel plates is 2 x 102 N/C.

Question 1:  What does the electric field intensity become when the distance between the plates is doubled.

Answer:  Since the electric field intensity depends only on the magnitudes of the charges on the plates, the electric field intensity does not change (ε = 2 x 102 N/C).

Question 2:  What does the electric field intensity become when the charge on the plates is doubled.

Answer:  Since the electric filed depends only on the magnitudes of the charges on the plates, the electric field intensity is also doubled (ε = 4 x 102 N/C).

 

V: Potential difference between the two plates (J/C, Volt, V)

 

d: distance between the plates (m)  (d must be not too much)

 

Fe = qt.ε  (Electric force is constant in the space between the parallel plates)

 

 

Since force is constant, acceleration is also constant:

 

Work:  W = FE. d

Work:  W = ∆E = q.∆V

 

Electric filed does not depends on the amount of space between the plates.

 

V: Potential difference between the two plates (J/C, Wolt, V)

d: distance between the plates (m)  (d must be not too much)

 

 

Oil drop experiment in parallel plates:

 

Gravitational force on the oil:  Fg = m.g [down]

 

Electric force on the oil drop:  Fe = qt.ε [up]

 

This forces must be equal to stay oil drop in still: 

Fg = Fe

m.g = qt

 

 

m:  Mass of the oil drop (kg)

Charge of one electron:  1 e- = - 1.602 x 10-19 C

Charge of one proton:   1.602 x 10-19 C

 

 

since

 

then

 

 

 

 

LIGHTNING AND LIGHTNING ROD

 

The charge is found on the surface of the conductor.  The charge will accumulate where the radius of curvature is smallest on irregular shaped objects.  Electric field is perpendicular to the surface of the conductor.

 

The tip of a lightning rod is small, so it creates a large electric field near its surface.

 

Small sphere and large sphere are connected together:

Small sphere:  charge: q,  radius:  r

Large sphere:  charge: Q,  radius:  R

 

Vsmall = Vlarge

 

 

 

 

 

ELECTRIC CURRENT:

 

the number of electrons in coulomb flowing past a given point in one second.

 

 

I:  Electric current (C/s, ampere, A)

Q:  Total charge (C)

∆t:  time taken for the charge to pass a certain point (s)