NEWTON LAWS OF MOTION

Tension

2 Topics
Quizzes on Newton Laws of Motion

5 Quizzes
FRICTION

Friction

2 Topics
Quizzes on Friction

5 Quizzes
VELOCITY AND ACCELERATION

CENTRAL FORCES

Equivalent One Body Problem

3 Topics
Types of Central Force Motion

4 Topics
Problems on Central Forces

4 Topics
Gravitational Field

4 Topics
Gravitational Potential

3 Topics
Gravitational Potential Energy

5 Topics
Quizzes on Central Forces

5 Quizzes
UNIFORMLY ROTATING FRAME- CENTRIFUGAL AND CORIOLIS FORCES

Circular Motion

5 Topics
Coriolis Force

1 Topic
Quizzes on Circular Motion

5 Quizzes
CONSERVATION LAWS

Quizzes on Work, Power and Energy

5 Quizzes
CENTRE OF MASS AND VRIABLE MASS SYSTEMS

Centre of Mass

5 Topics
Quizzes on Centre of Mass

5 Quizzes
RIGID BODY DYNAMICS

Rotation about Fixed Axis

4 Topics
Translation + Rotation

6 Topics
Angular Momentum

4 Topics
Moment of Inertia Tensor

3 Topics
Quizzes on Rigid Body Dynamics

5 Quizzes
FLUID DYNAMICS

Fluid Statics

6 Topics
Fluid Dynamics

4 Topics
Euler Equations and Its Applications

4 Topics
Quizzes on Fluid Dynamics

5 Quizzes
COULOMB LAW AND ELECTRIC FIELD

Electric Field

3 Topics
Quizzes for Electric Field and Potential

4 Quizzes
GAUSS LAW OF ELECTROSTATICS AND APPLICATIONS

Gauss Law of Electrostatics

7 Topics
Quizzes on Gauss law of Electrostatics

2 Quizzes
Capacitance

3 Topics
POLARIZATION OF DIELECTRICS

Polarization of Dielectrics

3 Topics
Problems on Field Calculation

2 Topics
Boundary Condition of D and E

3 Topics
Quizzes on Polarization of Dielectrics

2 Quizzes
WORK AND ENERGY IN ELECTROSTATICS

Electrostatic Energy

4 Topics
Problems on Electrostatic Energy

3 Topics
Problems on Work and Energy

5 Topics
Electrostatic Energy in Dielectrics

2 Topics
Capacitors

3 Topics
Quizzes on capacitance

5 Quizzes
BOUNDARY VALUE PROBLEMS

Boundary Value Problems

3 Topics
Quizzes on Electrostatics

6 Quizzes
CURRENT ELECTRICITY

Electric Current and Resistance

3 Topics
Quizzes on Current Electricity

8 Quizzes
MAGNETOSTATICS

Quizzes on Magnetostatics

7 Quizzes
FARADAY LAW OF ELECTROMAGNETIC INDUCTION

Problems on Faraday Law

5 Topics
Quizzes on Faraday law

7 Quizzes
MAGNETIC MATERIALS

Ferromagnetism

1 Topic
DC CIRCUITS

LR circuit

2 Topics
LCR Circuit

1 Topic
AC CIRCUITS

AC Circuit

6 Topics
Quizzes on Alternating Current

5 Quizzes
MAXWELL EQUATIONS and poynting vector

Poynting Vector

3 Topics
ELECTROMAGNETIC WAVES

REFLECTION AND REFRACTION OF EM WAVES AT THE INTERFACE OF TWO DIELECTRICS

Kinematic Properties

3 Topics
Fresnel Formula

4 Topics
Section 3: MATHEMATICAL PHYSICS

MULTIPLE INTEGRAL

Change of Order

7 Topics
VECTOR CALCULUS

Divergence and Curl

4 Topics
Line Integral

4 Topics
Greens Theorem

6 Topics
Surface Integral

6 Topics
Gauss Divergence Theorem

8 Topics
Stokes Theorem

5 Topics
Conservative Vector Field

3 Topics
DIFFERENTIAL EQUATIONS

Orthogonal Trajectory

2 Topics
MATRICES

Introduction to Matrices

7 Topics
Linear Equations

6 Topics
Determinant

7 Topics
Revision of Matrices

6 Topics
Similar Matrices

1 Topic
Monotonicity

5 Topics
DIFFERENTIAL CALCULUS

Critical Points

3 Topics
Maxima and Minima

3 Topics
Lagrange Mean Value Theorem

3 Topics
Function of Two Variables

7 Topics
FOURIER SERIES

Fourier Series

1 Topic
PARTICLE NATURE OF WAVE

Photoelectric Effect

3 Topics
WAVE NATURE OF PARTICLE

Wave Nature of Particle

3 Topics
H ATOM

H atom and X-rays

1 Topic
Quizzes on Origin of Quantum Mechanics

5 Quizzes
POSTULATES OF QUANTUM MECHANICS

Postulates of Quantum Mechanics

8 Topics
Problems on Postulates

3 Topics
SCHRONDINGER WAVE EQUATION

Quizzes on Schrodinger Wave Equations

5 Quizzes
NUCLEAR PHYSICS

Problems on Radioactive Decay

2 Topics
Quizzes on Nuclear Physics

5 Quizzes
SPECIAL THEORY OF RELATIVITY

Problems on Relativity

3 Topics
Quizzes on Special Theory of Relativity

3 Quizzes
SIMPLE HARMONIC OSCILLATION

Quizzes on Simple Harmonic Motion

4 Quizzes
DAMPED AND FORCED OSCILLATION

Forced Oscillation

4 Topics
WAVES

Waves

4 Topics
Quizzes on Waves

5 Quizzes
GEOMETRICAL OPTICS

Fermat Principle

1 Topic
Thin Lens

2 Topics
INTERFERENCE

Young Double Slit Experiment

7 Topics
Thin Films

2 Topics
Quizzes on Interference

4 Quizzes
DIFFRACTION

Single Slit

2 Topics
Double Slit

2 Topics
POLARIZATION OF LIGHT

Problems on Polarization of light

2 Topics
Quizzes on Polarization

3 Quizzes
THERMAL EXPANSION

CALORIMETRY

TRANSMISSION OF HEAT

**Trajectory**

A curve which cuts every member of a given family of curves in accordance with some given law, is called trajectory of the given family of curves.

**Orthogonal Trajectory**

If a cuts every member of given family of curves at right angle it is called orthogonal trajectory.

As an example y = mx and are respectively the family of straight line and family of circles with centre or origin and radius a.

Every line y = mx cut each member of family of circles at right angle.

So y = mx is orthogonal trajectory of

**Determination of orthogonal trajectories in cartesiancoordinates**

**Working Rule.**

1. Differentiate the given equation of family of curves. Eliminate the parameters between the derived equation and given equation of the family. It will give the differential equation of given family of curve.

2. Replace dy/dx (slope of tangent) by –dx/dy (slope of orthogonal family) in the above differential equation in step 1.

3. Obtain the general solution of differential equation in step 2.

**Self orthogonal family of Curves**

If each member of a given family of curves intersects all other members orthogonally, then given family of curves is said to be self orthogonal.

Let the equation of given family of curves be f(x, y, c) = 0 …(1)

Differentiate (1) w.r.t x and eliminate c between (1) and derived equation

We shall arrive at the differential equation of given family as F(x, y, dy/dx) = 0 …(2)

Let be the angle, which the tangent at P to the member PQ with x axis.

Then …(3)

Let (X, Y) be the current coordinates of any point of a trajectory. At point of intersection P of any members of (2) with the trajectory , let be the angle which the tangent to the trajectory makes with x axis.

So, …(4)

Let PT and PT’ intersect at 90°.

So

At the point of intersection x = X and y = Y

So , is the required family of trajectories.

**Determination of orthogonal trajectories in polarcoordinate system**

Let the equation of given family of curves be in polar form …(1)

Where c is a parameter

Differentiate (1) w.r.t and eliminating c between (1) and derived equation. We get the differential

equation of the given family of curves.

Let be that differential equation …(2)

Let be the angle between the tangent PT to a member PQ of the given family of curves and radius vector OP at any point .

then …(3)

Let be the current coordinates of any point of a trajectory. At point of intersection P of any member of (2) with the trajectory PQ’, let be the angle which the tangent PT’ to the trajectory makes with the common radius vector OP.

Then

Let PT and PT’ intersect at 90°

Then

So using (3) and (4)

At the point of intersection r = r’ and

So is the required orthogonal trajectory.

**Determination of Orthogonal trajectories in PolarCoordinates**

**Working Rule :**

1. Differentiate the given equation of family of curves w.r.t (generally take logarithm). Eliminate the parameter.

2. Replace by and obtain the differential equation of orthogonal trajectories

3. Obtain the general solution of differential equation obtained above.

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