Aakash IIT-JEE - Corporate Office : Aakash Tower, Plot No. 4, Sector-11, Dwarka, New Delhi-75 Ph.: 45543147/8 Fax : 25084119 (1) ELECTROSTATICS Electrostatics is the branch of electromagnetism where we study charges at rest. It actually means that either they are at rest or moving with constant velocity. Electric Charge It is the inherent property of certain fundamental particles. It accompanies them whereever they exist. Commonly known charged particles are proton and electron. The charge of a proton is taken as positive and that of electron is taken as negative. It is represented by symbol e. e = 1.6 × 10 –19 coulomb Charge of proton = +e Charge of electron = –e Positive and negative sign were arbitrarily assigned by Benzamin Franklin. This does not mean that charge of proton is greater than charge of electron. Properties of Electric Charge (1) Charges interact with each other i.e., they exert force on each other. Like charges do not like (repel) each other while unlike charges like each other (attract). (2) Charge is of two kind : Positive and negative. (3) Total charge of an isolated system is conserved (Consevation of charge) (4) Charge is quantised (5) Charge can be transferred : Charge can be transferred from one body to other. This occurs due to transfer of electrons from one body to other. One of the common example of transfer of charge is charging by friction. Electrostatics CHAPTER AIEEE Syllabus Electric charges: Conservation of charge, Coulomb’s law-forces between two point charges, forces between multiple charges; superposition principle and continuous charge distribution. Electric field: Electric field due to a point charge, Electric field lines, Electric dipole, Electric field due to a dipole, Torque on a dipole in a uniform electric field. Electric flux, Gauss’s law and its applications to find field due to infinitely long, uniformly charged straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell. Electric potential and its calculation for a point charge, electric dipole and system of charges; Equipotential surfaces, Electrical potential energy of a system of two point charges in an electrostatic field. Conductor and insulator, Dielectric and electric polarisation, Capacitor, Combination of capacitor in series, in parallel, Capacitance of parallel plate capacitor and without dielectric medium between the plates, energy stored in capacitor. THIS CHAPTER COVERS : Electric Charge and its Properties Coulomb’s Law Electric Field Electric Lines of Force Electric Field due to Electric Dipole Electric Dipole in Uniform Electric Field Electric Flux Gauss’ Law and its Applications Electric Potential and electrostatic Potential Energy Electric Capacitor Parallel Plate Capacitor with Dielectric and Conducting Slab Energy Stored in the Capacitor Capacitors in Series and Parallel Combinations www.puucho.com Study More with www.puucho.com
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Electrostatics is the branch of electromagnetism where we study chargesat rest. It actually means that either they are at rest or moving with constantvelocity.
Electric Charge
It is the inherent property of certain fundamental particles. It accompaniesthem whereever they exist. Commonly known charged particles are protonand electron. The charge of a proton is taken as positive and that of electronis taken as negative. It is represented by symbol e.
e = 1.6 × 10–19 coulomb
Charge of proton = +e
Charge of electron = –e
Positive and negative sign were arbitrarily assigned by Benzamin Franklin.This does not mean that charge of proton is greater than charge of electron.
Properties of Electric Charge
(1) Charges interact with each other i.e., they exert force on each other.Like charges do not like (repel) each other while unlike charges like eachother (attract).
(2) Charge is of two kind : Positive and negative.
(3) Total charge of an isolated system is conserved (Consevation ofcharge)
(4) Charge is quantised
(5) Charge can be transferred : Charge can be transferred from one bodyto other. This occurs due to transfer of electrons from one body to other.One of the common example of transfer of charge is charging by friction.
Electrostatics
C H A PT E RAIEEE Syllabus
Electric charges: Conservation of charge, Coulomb’s law-forces between
two point charges, forces between multiple charges; superposition principle
and continuous charge distribution. Electric field: Electric field due to a point
charge, Electric field lines, Electric dipole, Electric field due to a dipole, Torque
on a dipole in a uniform electric field. Electric flux, Gauss’s law and its
applications to find field due to infinitely long, uniformly charged straight
wire, uniformly charged infinite plane sheet and uniformly charged thin
spherical shell. Electric potential and its calculation for a point charge,
electric dipole and system of charges; Equipotential surfaces, Electrical
potential energy of a system of two point charges in an electrostatic field.
Conductor and insulator, Dielectric and electric polarisation, Capacitor,
Combination of capacitor in series, in parallel, Capacitance of parallel plate
capacitor and without dielectric medium between the plates, energy stored
Frictional Electricity : When two bodies are rubbed with each other, they are found to attract each other.This is so because, on rubbing, transfer of electrons takes place from one body to other. One of themacquires a positive charge and other acquires a negative charge.
A BRubbing
e–
Transfer
Neutral Neutral
(6) Charge is invariant : Charge of a particle is independent of speed.
(7) Charge cannot exist without mass, while mass can exist without charge.
INTERACTION BETWEEN CHARGES
Coulomb’s Law
It gives an expression for the force between two charged particles or particles like objects.
221
01212 4
1||||
r
qqFF
q1 q2
F21F12 r
where, 229
0
/CNm1099.84
1
0 = 8.85 × 10–12 C2/m2N. This is called absolute permittivity of free space.
Important Points :
1. If q1q2 > 0, force is repulsive.
2. If q1q2 < 0, force is attractive.
3. This force is central and conservative.
4. This force is between two charges and is independent of the presence of other charges i.e., if some othercharges are present in the region, the force between two given charges remains same.
Coulomb’s Law in Vector Form
ix
qqF ˆ
4
12
21
012
, i
x
qqF ˆ
4
12
21
012
F12
q1 q2
F21
x-axis
x
ELECTRIC FIELD
This space around a charge distribution, in which the charge can exert force on other charges is called electricfield.
Electric Field Intensity
We define electric field intensity at a point as the force experienced per unit charge when a very small positivetest charge is placed at that point.
q
FE
q
0Limit
Units : SI units of electric field intensity are (i) N/C (ii) volt/metre
(3) Two field lines do not intersect each other, as at point of interaction, we will get two different directionsof electric field which is not possible.
(4) They contract longitudinally on account of attraction between opposite charges.
(5) They exert lateral pressure on each other on account of repulsion between like charges.
Following pattern of lines of force are not possible
1. +q 2. 3. 4.
ELECTRIC DIPOLE
An arrangement of two equal and opposite charges separated by some distance.
–q +q
p
2a
Dipole Moment
Dipole moment is a vector quantity directed from negative to positive charge. It is represented by p .
Its magnitude is p = (2a) × q
Units : C-m [coulomb-metre]
The most practical example of an electric dipole is a water molecule.
105° Hydrogen
Oxygen
Hydrogen
p
p
Ideal Dipole
An ideal dipole is a short dipole with large value of q and negligible value of 2a.
In c.g.s. system, units of dipole moment is Debye.
The field due to a point charge is spherically symmetric. So if we draw a gaussian sphere around thecharge, the strength of electric field will be same every where. Using above formula