Physics important points

:label: Some Basic Results of Vector Calculus:

  1. Vectors in the same direction can be added by simply adding their magnitudes. But if the vectors to be added are in opposite directions, then their magnitudes are subtracted and not added.

  2. Column vectors can be added by simply adding the values in each row.

  3. You can find the magnitude of a vector in three dimensions by using the formula a2 = b2 + c2 + d2, where a is the magnitude of the vector, and b, c, and d are the components in each direction.

  4. If l1a + m1b = l2a + m2b then l1 = l2 and m1 = m2

  5. Collinear Vectors are also parallel vectors except that they lie on the same line.

  6. When two vectors are parallel, the dot product of the vectors is 1 and their cross product is zero.

7)Two collinear vectors are always linearly dependent.

  1. Two non-collinear non-zero vectors are always linearly independent

  2. Three coplanar vectors are always linearly dependent.

  3. Three non-coplanar non-zero vectors are always linearly independent

  4. More than 3 vectors are always linearly dependent.

  5. Three vectors are linearly dependent if they are coplanar that means any one of them can be represented as a linear combination of other two.


:boom:Formulas related to force::boom:
☆F = ma
☆F = kx
☆F = m(vf² - vi²/2S)
☆F = mv/t
☆F = md/t²
☆F = m(vf - vi)/t
☆F = Area × density × velocity²
☆F = 1/2 mv²/d
☆F = 1/2 Pv/d
☆F = Power/velocity
☆Fc = mv²/r
☆Fc = mrw²
☆Fc/2 = mv²/2r
☆Fc = 2K.E/r
☆F = Area × Stress
☆F = pir² × stress
☆F = YA × Strain
☆F = YAl/L
☆F = pressure × area
☆F = change in momentum × time interval
☆F = - 2mVx × Vx/2l
☆F2 = F1/A1 × A2
☆F = qE
☆F = kQ/r²
☆F = ILB sintheta
☆F = q (v × B)
☆F = qE + q(v × B)


Quick Revision Notes On : Liquids at Rest

Force of cohesion:- It is force between two molecules of similar nature.

Force of adhesion:- It is the force between two molecules of different nature.

Molecular range:- The maximum distance between two molecules so that the force of attraction between them remains effective is called molecular range.

Sphere of influence:- Sphere of influence of any molecule is the sphere with molecule as its center and having a radius equal to molecular range (=10-7 cm).

Surface film:- Surface film of a liquid is defined as the portion of liquid lying on the surface and caught between two parallel planes situated molecular range apart.

Surface tension:-

Surface Tension

Surface tension is the property of a liquid by virtue of which its free surface behaves like a stretched membrane and supports, comparatively heavier objects placed over it. It is measured in terms of force of surface tension.

Force of surface tension:- It is defined as the amount of force acting per unit length on either side of an imaginary line drawn over the liquid surface.

(a) T = Force/length = F/l

(b) T = Surface energy/Surface area = W/A

Units:- S.I – Nm-1

C.G.S- dyn cm-1

Additional force:-
(a) For a cylindrical rod:- F = T×2πr (Here r is the radius of cylindrical rod)

(b) For a rectangular block:- F = T×2(l+d) (Here l is the length and d is the thickness of the rectangular block)

(c) For a ring:- F = T×2×2πr (Here r is the radius of cylindrical rod)

Surface energy:-
Potential energy per unit area of the surface is called surface energy.

(a) Expansion under isothermal condition:-

To do work against forces of surface tension:-

W= T×A (Here A is the total increase in surface area)

To supply energy for maintaining the temperature of the film:-

E = T+H

(b) Expansion under adiabatic conditions:-

E = T

Force of surface tension is numerically equal to the surface energy under adiabatic conditions.

Drops and Bubbles:-

(a) Drop:- Area of surface film of a spherical drop of radius R is given by, A = 4πR2

(b) Bubble:- The surface area of the surface films of a bubble of radius R is, A = 2×4πR2

Combination of n drops into one big drop:-

(a) R = n1/3r

(b) Ei = n (4πr2T), Ef =4πR2T

(c) Ef/ Ei = n -1/3

(d) ΔE/Ei = 1-(1/n1/3)

(e) ΔE = 4πR2T (n1/3-1) = 4πR3T (1/r – 1/R)

Angle of contact:- Angle of contact, for a pair of solid and liquid, is defined as the angle between tangent to the liquid surface drawn at the point of contact and the solid surface inside the liquid.

(a) When θ < 90º (acute):-

Fa >Fc/√2

(i) Force of cohesion between two molecules of liquid is less than the force of adhesion between molecules of solid and liquid.

(ii) Liquid molecules will stick with the solid, thus making solid wet.

(iii) Such liquid is put in the solid tube; it will have meniscus concave upwards.

(b) When θ > 90º (obtuse):-Fa<Fc/√2

(i) Force of cohesion between two molecules of liquid is less than the force of adhesion between molecules of solid and liquid.

(ii) In this case, liquids do not wet the solids.

(iii) Such liquids when put in the solid tube will have a meniscus convex upwards.

(c) When θ = 90º:-?


The surface of liquid at the point of contact is plane. In this case force of cohesion and adhesion are comparable to each other.

(d) cosθc = Tsa – Tsl/Tla

Here, Tsa,Tsl and Tla represent solid-air, solid-liquid and liquid-air surface tension respectively). Here θc is acute if Tsl < Tsa while θc is obtuse if Tsl >Tsa.


?Rise of Liquid in a Capillary Tube?Capillarity is the phenomenon, by virtue of which the level of liquid in a capillary tube is different from that outside it, is called capillarity.

Weight of liquid, W = Vρg = πr2h+(r/3)ρg (Here r is the radius meniscus)

If weight of meniscus is taken into account, the force of surface tension will be,

T = r(h+(r/3)) ρg/2 cosθ

For fine capillary, force of surface tension, T = rhρg/2 cosθ

So height, h = 2T cosθ/ rρg

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:white_check_mark: Concave Mirrors:
By reflection of light, concave mirrors give real, inverted images if the object is beyond the focus and a virtual, erect, enlarged image if the object has a distance less than the focal length from the pole of the mirror.

:point_right:t2: Uses of Concave Mirrors:
:heavy_minus_sign: Concave mirrors are used in torches, searchlights, and headlights of vehicles to get powerful parallel beams of light.
:heavy_minus_sign: Concave mirrors are also used as shaving mirrors to see a larger image of the face.
:heavy_minus_sign: Dentists use concave mirrors to see bigger images of the teeth of the patients.
:heavy_minus_sign: Large concave mirrors are used to focus sunlight to produce heat in the solar furnaces.

:white_check_mark: Convex Mirrors:
By the reflection of light convex Mirrors always give a virtual, erect, diminished image of the object kept infront of the mirror.

:point_right:t2: Uses of Convex Mirrors:
:heavy_minus_sign: The convex mirror is used as a side-view mirror in vehicles to give a smaller view of the vehicles coming from behind.
:heavy_minus_sign: They are used in shops and supermarkets and any other place where there is a requirement for detecting burglars.
:heavy_minus_sign: Convex mirrors are used in making lenses for sunglasses.
:heavy_minus_sign: Convex mirrors are used in magnifying glasses, and telescopes.
:heavy_minus_sign: Convex mirrors are used to reflect street light; because they can reflect over a wide area.
:heavy_minus_sign: Convex mirrors are kept at the street corners to avoid collisions.


Electric Dipole Quick Review :hugs:

:small_red_triangle_down:The energy of electric dipole is given by U = – p.E.

:small_red_triangle_down:The energy of a magnetic dipole is U = – μ .B C.

:small_red_triangle_down:Electric Charge : Q = ± ne (e = 1.60218 × 10-29 C)

:small_red_triangle_down:SI unit of Electric Charge is Coulomb (C)

:small_red_triangle_down:Coulomb’s Law : Electrostatic Force (F) = k[q1q2/r2] and,
In Vector Form :

Where, q1 and q2 = Charges on the Particle,
r = Separation between them,
→r = Position Vector,
k = Constant = 14πϵ0=8.98755×109Nm2C2

:small_red_triangle_down:Electric Current :

The current at Time t : i=limΔt→0 ΔQ/Δt= dQ/dT
Where Δ Q and Δ T = Charges crosses an Area in time Δ T
SI unit of Current is Ampere (A) and 1A = 1 C/s

:small_red_triangle_down:Average current density:
j=limΔs→0 Δi/Δs=di/dS ,
Where, Δ S = Small Area,
Δ i = Current through the Area Δ S,
P = Perpendicular to the flow of Charges,
θ = Angle Between the normal to the Area and the direction of the current.

:small_red_triangle_down:Kirchhoff’s Law:
Law of Conservation of Charge: I3 = I1 + I2

:small_red_triangle_down:Resistivity : ρ(T)=ρ(T0)[1+α(T−T0)]
R (T) =R (T0) [1+α (T−T0)]
Where, ρ (T) and ρ (T0) = Resistivity at Temperature T and T0 respectively,
α = Constant for given material.

:small_red_triangle_down:Lorentz Force :
Where, E = Electric Field,
B = Magnetic Field,
q = Charge of Particle,
v = Velocity of Particle.

:small_red_triangle_down:Magnetic Flux:

Magnetic Flux through Area dS = ϕ=→B⋅d → S= B⋅dS Cos θ
Where, d→S = Perpendicular vector to the surface and has a magnitude equal to are Ds,
→B = Magnetic Field at an element,
θ = Angle Between →B and d→S,
SI unit of Magnetic Flux is Weber (Wb).


Electric Charges and Fields

  1. Electric Charge Charge is the property associated with matter due to which it produces and experiences electric and magnetic effect.

  2. Conductors and Insulators Those substances which readily allow the passage of electricity through them are called conductors, e.g. metals, the earth and those substances which offer high resistance to the passage of electricity are called insulators, e.g. plastic rod and nylon.

  3. Transference of electrons is the cause of frictional electricity.

  4. Additivity of Charges- Charge are scalars and they add up like real numbers. It means if a system consists of n charges q1, q2, q3 , … ,qn, then total charge of the system will be q1 +q2 + … +qn.

  5. Conservation of Charge The total charge of an isolated system is always conserved, i.e. initial and final charge of the system will be same.

  6. Quantisation of Charge -Charge exists in discrete amount rather than continuous value and hence, quantised.

Mathematically, charge on an object, q=±ne
where, n is an integer and e is electronic charge. When any physical quantity exists in discrete packets rather than in continuous amount, the quantity is said to be quantised. Hence, charge is quantised.

  1. Units of Charge
    (i) SI unit coulomb (C)
    (ii) CGS system
    (a) electrostatic unit, esu of charge or stat-coulomb (stat-C)
    (b) electromagnetic unit, emu of charge or ab-C (ab-coulomb)
    1 ab-C = 10 C, 1 C = 3 x 109 stat-C
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Laws of Motion.
Work, Energy, and Power.
Heat & Thermodynamics.
Rotational Motion.
Modern Physics.
Current Electricity & Magnetism.


✰ System -

Part of the universe under investigation.

✰ Open System -

A system which can exchange both energy and matter with its surroundings.

✰ Closed System -

A system which permits passage of energy but not mass, across its boundary.

✰ Isolated system -

A system which can neither exchange energy nor matter with its surrounding.

✰ Surroundings -

Part of the universe other than system, which can interact with it.

✰ Boundary -

Anything which separates system from surrounding.

✰ State variables -

The variables which are required to be defined in order to define state of any system i.e. pressure, volume, mass, temperature, surface area, etc.

✰ State Functions -

Property of system which depend only on the state of the system and not on the path. Example: Pressure, volume, temperature, internal energy, enthalpy, entropy etc.

✰ Intensive properties -

Properties of a system which do not depend on mass of the system i.e. temperature, pressure, density, concentration,

✰ Extensive properties -

Properties of a system which depend on mass of the system i.e. volume, energy, enthalpy, entropy etc.

✰ Process -

Path along which state of a system changes.

✰ Isothermal process -

Process which takes place at constant temperature

✰ Isobaric process -

Process which takes place at constant pressure

✰ Isochoric process -

Process which takes place at constant volume.

✰ Adiabatic process -

Process during which transfer of heat cannot take place between system and surrounding.

✰ Cyclic process -

Process in which system comes back to its initial state after undergoing series of changes.

✰ Reversible process -

Process during which the system always departs infinitesimally from the state of equilibrium i.e. its direction can be reversed at any moment.

✰ Irriversible Process -

This type of process is fast and gets completed in a single step. This process cannot be reversed. All the natural processes are of this type.