Electric charges
Definition
Physical property of matter which experiences a force when kept in electromagnetic field
Like charges repel and unlike attracts
-When a glass rod is rubbed with silk, glass rod becomes positively charged and silk negaitive.
• When a plastic rod is rubbed with fur, plastic rod becomes negatively charged and fur positive.
1.Electric charges are of two kinds –
positive and negative.
2.Like charges repel and unlike charges attract each other.
3.Charge is a scalar quantity.
Conductors and insulators
Conductors
Conductors are those substances which allow passage of electricity through them.
Eg. Metals, human and animal bodies and earth are conductors.
• They have electric charges (electrons) that are comparatively free to
move inside the material.
• When some charge is transferred to a conductor, it readily gets
distributed over the entire surface of the conductor.
▪ Metals cannot be charged by friction,because the charges transferred to the metal leak through our body to the ground as both are conductors of electricity.
Insulators
The substances which offer high resistance to the passage of electricity through them are called Insulators .
Eg. glass, porcelain, plastic, nylon, wood
▪ If some charge is put on an insulator, it stays at the same place. So insulators gets electrified on combing dry hair or on rubbing,
Earthing or grounding
When a charged body is brought in contact with earth, all the excess charge pass to the earth through the connecting conductor. This process of sharing the charges with the earth is called grounding or earthing
Methods of Charging
1) Charging by friction
When two bodies are rubbed each other, electrons in one body (in which electrons are held less tightly) transferred to second body (in which electrons are held more tightly)
When a glass rod is rubbed with silk, some of the electrons from the glass are transferred to silk. Hence glass rod gets +ve charge and silk gets -ve charge.
2) Charging by conduction
Charging a body with actual contact of another body is called charging by conduction. If a neutral conducting body (A) is brought in contact with positively charged conducting body (B), the neutral body gets positively charged.
3)Charging by induction
When a charged body is brought near to an uncharged conductor (without touching), that end of the uncharged conductor which is near to the charged body gets oppositely charged and the farther end is charged with the same type of charge.
Properties of electric charges
1)charge are quantised:
According to quantisation of electric charge, charge of a body is an integral multiple of a basic charge, which is the electronic charge.
Charge on a body, q=± ne ; where, n=1,2,3.........
e is the electronic charge. e=1.602 x 10−19 C
2)Charges are conserved:
It means that total charge of an isolated system remains constant. It also implies that electric charges can neither be created nor destroyed.
3)charges are additive:
The total charge on a surface is the algebraic sum of
individual charges present on that surface.
If q1, q2 , q3....................., qn are the charges on a surface, then total or net charge,
𝒒 = 𝒒𝟏 + 𝒒𝟐 + 𝒒𝟑 +.................. + 𝒒𝒏
Coulomb’s Law
Definition
States that, The electrostatic force between two point charges are directly proportional to the magnitudes between them and inversely proportional to the distance between them
Coulomb’s law in vector form
Superposition principle
Definition
Force on a charge due to a number of charges is the vector sum of forces
due to individual charges.For a system of n charges.
Electric Field
Definition
Electric field is the region around a charge where its effect can be felt.
Formula
F=qE
Vector quantity
SI unit = N/C
Electric field due to a point charge
Electric Field Lines
Definition
An electric field line is a curve drawn in such a way that the tangent to it at each point is in the direction of the net field at that point.
Properties
1. Electric Field lines start from positive charge, end at negative charge.
2. Electric field lines of a positive charge are radially outwards and that of a negative charge is radially inwards
3. Electric field lines do not form closed loops.
4. In a charge free region field lines are continuous.
Two field lines never intersect.( Two directions for electric field is not possible at a point)
5. Field lines are parallel ,equidistant and in same direction in uniform electric field.
Types of Electric Field Lines
Electric Flux
Definition
Electric flux associated to a surface is the number of field lines passing normally through the surface
Dipole
Definition
An electri dipole is a pair of equal and opposite charges separated by a distance
The total charge of the system is +q + -q =0
Electric Dipole moment (𝐩⃗ )
Product of magnitude of one charge n distance between them
P=qx2a
q= magnitude of charge
2a= distance between them
Unit = Cm
Vector quantity
Electric Field duo to a Dipole along the Axial Line
Electric Field duo to a Dipole along the Equatorial Line
Relation connecting Axial field and Equatorial field of a Dip
Dipole in a Uniform External field
In a uniform electric field there will be a net torque on the dipole, but the net force will be zero. Due to the torque ,the dipole rotates. There will be no translatory motion as the net force is zero.
Continuous Charge Distribution
Linear charge density
The linear charge density λ of a wire is defined as
Line charge q = 𝝀𝒍
The unit of λ is C/m
Surface charge density
The surface charge density 𝜎 of a area element is defined as
Surface charge, q= 𝝈𝑺
The units for σ is C/𝑚2
Volume charge density
The volume charge density ρ of a volume element is defined as
Volume charge , q= 𝛒𝑽
The units for ρ is C/𝑚3
Gauss’ theorem
Definition
Gauss’s theorem states that the total electric flux through a closed surface is equal to 𝟏/E0 times the total charge enclosed by the surface.
Surface over which we calculate the fluux is callled Gaussian surface
Features of gauss law
1)Gauss law is true for any surface irrespective of their sizes and shape
2)charges include sum of all the charges enclosed by the surface
3)gauss law useful to calc field when the system has some symmetry
4)gauss law is based on the inverse square dependence onnn distance contained in the Coulomb’s law
Applications of gauss law
1) Electric field due to an infinitely long straight uniformly charged wire
2)Electric field due to a uniformly charged infinite planesheet
3)Electric field due to a uniformly charged thin spherical shell
a)field outside the shell
b)field on the surface of the shell
Example 2
A comb drawn through person’s hair causes 1022 electrons to leave the person’s hair and stick to the comb. Calculate the charge carried by the comb.
q= ne,
q = 10^22 x 1.602 x 10^-19C
= −1.602 x 10^3 C
As the comb gains electrons it gets negatively charged.
EXAMPLE 1
How many electronic charges form 1 C of charge?
q=±ne,
n=𝑞 𝑒
n= 1 1.602 x 10^-19
=6.25 x10^18
Gold Leaf Electroscope
A simple apparatus to detect charge on a body is called a gold-leaf electroscope.
Apparatus It consists of a vertical metal rod placed in a box. Two thin gold leaves are attached to its bottom end as shown in figure.
Working
When a charged object touches the metal knob at the top of the rod, charge flows on to the leaves and they diverge. The degree of divergence is an indicator of the amount of charge.
How is frictional electrification caused?
The number of protons inside the nucleus of an atom is equal to the number of electrons outside the nucleus. When a body is rubbed with another, due to friction, some electrons from one body gets transferred to the other body. The body, which loses electrons, will become positively charged and which gains electrons becomes negatively charged. The two bodies thus acquire opposite charges and they are equal in magnitude. This is the reason for frictional electricity.
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