Class 12 ELECTROSTATICS

Class 12 ELECTROSTATICS

CHAPTER-1

ELECTRIC CHARGES AND FIELDS

Electric Charge (e)

 → It is an instrinsic property of elementary particles of matter which gives rises to electric force b/w various objects.

 → Scalar quantity

 → S. I. unit Cola Couloumb (C)

 → Minimum charge : e = 1.6×10-19 C

 → smaller unit is micro coulomb (μC), 1μC=106C

 →(Pico) micro, micro coulomib (μμc) = 1012C

Electrostatics

 Study of electric charges at rest.

 Application

 i) In electrostatic loudspeaker.

 ii) In flush collection in chimneys.

 iii) In Xerox coping machine

✤ 2 kinds of Electric Charges

         i) Positive            ii) Negative

 i) Protons :- Acquired positive charge, as it has tendency to loose electrons charge particles.

                          e=1.6x10⁻¹⁹C, mass = 1.67x10⁻²⁷ kg

 ii) Electrons :- Acquired negative charge, as it has tendency to gain charge particles

                          e=1.6x10⁻¹⁹C, mass = 9.1x10⁻³¹ kg

✤ 2 kinds of charge developed on rubbing

              Positive charge                              Negative charge

                    Glass rod                                      Silk cloth

                  Flannel on cat skin                      Ebonite rod

                   Woolen cloth                              Amber rod

                   Woolen coat                                Plastic seat

                  Woolen carpet                              Rubber shoes

For Your knowledge

         → Cause of charge transfer of e- from material to another while rubbing, e+ doesn't transfer

         → Low work function loses electrons & become e+ charge

         → As e- has finite mass, So while +charge body ↓es mass.

         → Change body ↑es mass.

Conductors - Substance through which electric charges can flow easily are called conductor

         Ex → Metals, human, graphite, etc.

              → Contain free e-.

Insulators - Substance through which electric charges cannot flow easily are called conductor.

             → e- are highly bound with nucleus, high resistance

         Ex → glass, nylon, plastic, etc.

Earthing - Process in which a body shares its charge with the earth.

                     House using 3-core wiring: live, neutral & earthing

Electrostatic Induction: - Phenomenon of temporary electrification of a conduction in which opp. changes appear at its classes end & similar charges

                    appear at its farther end in the presence of a nearby charged body.

For Your knowledge

             Gold leaf-electroscope is a device used for detecting an electric change and identifying its polarity.



Basic Properties of Electric Change

i) Additivity of electric charge: Total charge of a system is the algebraic sum of all individual charge located at different point inside the system.

                                          Q = Q1 + Q2 + Q3 -------- Qn

Note:    1. unit of charge is coulomb or stat coulomb; 1C=3X109 stat coulomb

             2. e.m.u. 3x10stalcoulomb

ii) Quantization of electric charge: Change is always fund in the form of integral multiple of a certain minimum charge.

                Q = ±ne

                        Total charge = ±no. of electron X minimum charge

        §. Quantization is applied for microscopic charge not in macroscopic.

Property of charge:

iii) Conservation of charge

→ Total charge of an isolated system remains constant.

→ Electric charge can neither be created non destroyed, they can only be

 transfer from one body to another.

→ Total charge of the entire universe remain constant.

2. Quantization of charge: It states that charge is always found in the form of integral multiple of charge on electron q = ±ne here n ∈ z

Difference b/w Mass & Electric charges

  Electric Charge

i) May be +, - or 0

ii) Always quantized

iii) Changes don't depend on speed

iv) Charges are strictly conserved.

v) Electrostatic force btw 2 charges may be attractive or repulsive.

  Mass

i) Always positive

ii) Quantized of mass not

iii) Mass ↑es with speed

iv) Mass is not conserved

v) Gravitational forces btw 2 masses are always attractive.

Coulomb's Law: - states that force of attraction on repulsion b/w 2 stationary point charges is directly proportional to the product of magnitudes of 2 charges and inversely proportional to square of distance b/w them.

   F = (Kq1 q2)/r2                               or              F = 1/4πε.(Kq1 q2)/r2

  Electrostatic Force constant(K)                      permittivity of free space(ε)

     k = 9x10⁹ Nm²c⁻² = 1/4πε₀ ,                          ε₀ = 8.85 x10⁻¹² c²N⁻¹m⁻²

    Conditions for coulomb's law:                      [M-1L-3T-4A2](Kq_1 q_2)/r^2 

1. Charged should be microscopic.

2. charge should be in rest.

3. Force is measured by TORSION balance device.

Property of coulomb's force:

1. It is a conservative force.

2. It is a centralized force,

3. Force btw two charges is not affected by the presence of other charge.

For Your Knowledge

→ Torsion balance is a sensitive device to measure force.

→ Coulomb's law is valid only for point charge

§. dielectrics are insulating materials which transmits electric effect without conducting.

Dielectic Constant : Relative Permitivity

It's an property of the medium which determines the electric force btw 2 charges situated in that medium.

k = ε / ε₀ = ε₀ / Fvac k(vaccum) = 1

k = F₀ / FmEd k(air) = 1.00054

Fmed

charges in air k(water) = 80

Dielectric strength: → The maximum value of electric field (dV/dr) that a dielectric material can tolerate without its electric breakdown.

Comparing Electrostatics & Gravitational forces

                  Similarities                                                       Disimilarities

i) Both follows inverse square law.                      i) G.F is attractive while EF

            F α 1/r²                                                          may be attractive on repulsive

ii) Both are proportional to product                      ii) G.F does not depend upon

    of masses or charges.                                           nature of medium, but EF does.

iii) Both are central forces.                                  iii) EF is much stronger than G.F.

iv) Both are conservative force. 

v) Both are operate in vaccum.

Note: Resultant of two forces F = √(F₁² + F₂² + 2F₁F₂Cosθ)

If θ = 0° then F = F₁ + F₂ (max)

If θ = 180°, then F = F₁ - F₂

Electric Field: (introduced by Faraday) At a point. Is defined as the electrostatics force per unit test charge acting on a vanishingly small positive test charge placed at that point.

→ Vector quantity          ε = lim(q∘→0)⁡[F/q0] (N/C or V/m) [MLT⁻³A⁻¹]

                                3 Path of charge in E is Parabolic. If θ=90°

Electrostatic force = charge x Electric Field

                  1. F = qE 2. Acceleration in charge a = qE/m (m-> mass)

Properties of Electric Field Lines

    i) These are imaginary lines.

    ii) They start from +ve and are ends at -ve.

    iii) They are continuous curve.

    iv) They are ⊥ to the surface of a charged body.

    v) Tangent to the lines gives the direction of electric field at that point.

    vi) They do not cut (intersect) each other because at the intersection point, we can draw 2 tangent which represent 2 directions of 'E' which is not                     possible.

    vii) No. of electric field lines represent the strength of E ⃗ at that point.

Electric Field due to point charge at r distance is

ε = 1/4πε.(Kq_1 q_2)/r^2 (N/C or V/m)

Continuous Charge Distribution

i) Volume charge distribution : 

         ρ = dq/dv (C/m³) [v→vol] 

ii) Surface charge distribution :

σ = dq/ds (C/m²) [s→area]

iii) Line charge distribution :

λ = dq/dL (C/m) [l→length]


        1. E by +ve charge is radially outward

         2. by -ve charge inward

Electric Dipole: A pair of equal & opposite point charges separated by a small distance is called an electric dipole.

 Dipole moment → |p=q×2a| (Cm)

 1. It is a vector Quantity

 2. direction of dipole is -ve to +ve charge

 3. Net charge on dipole is zero.

✤ Ideal on point charge dipole of negligibly small size is called an ideal or point dipole. (2a→0)

    lim. formula [M0LTA]

Electric Field at an Axial point of a Dipole


 ε= 1/4πε . (p X 2r)/(r2- a2 )2 or ε= 1/4πε . 2p/r3

Electric field at an Equitorial point of a Dipole

                 ε= 1/4πε . P/(r2+a2 )(3/2)              or                 ε= 1/4πε . P/r3

                                                                                         for short dipole.

           εaxialeq = 2/1                              or              εaxial= 2 εequatorial

Torque on a Dipole in a Uniform Electric field

          τ= pEsinθ (Nm)

          → vector quantity.

          Notes :If θ=0°

          1. then dipole is in stable equilibrium. (τ=0)

          2. If θ=180° then dipole is in unstable equilibrium and [τ=0]

                   energy=pE                 U = PE cosθ

          3. Net force on dipole in uniform E is zero

Notes : in non uniform E, Net force is non zero but torque does not act to zero.

Electric Field Lines for Different Change Conductors

i) Field lines of a positive point charge


ii) Field line of -point charge


iii) Field lines of 2 equal opp. point charge


iv) Field lines of 2 equal & +point charge


v) Field lines of a positively charged plane conductor.


Electric Flux: Through a given area held inside an electric field is the measure of the total no. of electric lines of forces passing normally through that a area Scalar quantity

         ΔΦΕ- EΔS cos theta - E. AS

         Φε= (E. ds (Nm²/c)

        Dimension = [M'L3T-3A-1]

Note: It is a scalar Quantity. It may be +ve or-ve.

            Φ=πR²E

Gauss's Law

It states that total electric flux passing through a closed surface is always equal to the times the total charge contains by the closed body.

Q = q / ε [ Nm²/C]

Note: Flux does not depend upon the shape and size of closed surface.

Note: If dipole is placed in a closed body then No flux is produced.

 Electric Field produced by thin spherical shell.

 Outside point: ε=1/ 4πϵₒ . q/r2      For r > R

 At the surface: ε= 1/ 4πϵₒ . q/r2      For r = R

 Inside points : ε=0 For r

Electric field of an infinite-plane sheet of charge

          ε = σ/2ϵₒ uniform charge density surface

Electric field produced by uniformly charged wire

           ε = λ/2πϵₒr => linear charge density

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