Lesson Posted on 09 Jul IIT JEE/IIT - JEE Mains/Mathematics/Mathematical Induction
Introdutcion to Differntial equation
Raj Kumar
I am Six Sigma Black belt trained from American Society of Quality I am 2011 pass out in B.tech from...
The differential equation is that equation which contains.
Differntial
Independent variable
Dependent variable
Order of Differential equation: Order of highest order derivative.
The degree of the differential equation: Degree of highest order derivative.
General Solution:
It is a genearlized solution which contains finite no of the solution.
Particular Solution:
It is a particular solution which contains only one solution of the differntial equation.
read less
Lesson Posted on 18 Jun IIT JEE/IIT - JEE Mains/Physics/Electrostatics Electromagnetic Waves
Anshuman
I can teach every topic very easily and make it stronger for the students.
This is my lesson plan for the chapter of electrostatics.
Electrostatics- The chapter of electrostatics deals with another^{1} fundamental nature of particles, “Charge”, in particular charges at rest.
This Chapter is broadly divide in nine parts, parts of the chapter and time required for each are given in sequence as per lesson plan. The time required for completion of the chapter narrowly varies around 25 hours.
Serial no. | Topics | Time required (Hours) |
1 | Charge | 1 |
2 | Interaction of charges | 1 |
3 | Electric field | 4 |
4 | Electric potential Energy | 2 |
5 | Electric potential | 4 |
6 | Relationship between electric field and electric potential | 1 |
7 | Electric Dipole | 2 |
8 | Gauss’ Law | 4 |
9 | Capacitors | 6 |
Definition and Properties
Definition- It includes formal definiton of charge, the idea of charged bodies, +ve and –ve charges, the transfer of charges, attraction and repulsion of charged bodies.
Properties- The charge carriers, quantisation of charges, conservation of charges. Conductors, free electons and induced charages.
Coulomb’s law of electrostatic force, between two point charges. Coulomb’s law in vector form. Principle of superposition, Electrostatic force on a point charge due to surround chage distribution.
Dfinition of electic field due to a point charge. Calculation of electric field at a point in space using principle of superpositon for descrete distribution and continuous distribution of chages.
Continuous Distribution of charges. (Uniform distribution of chages )
Continuous distribution of charges ( Non uniform distribution)Demonstration of concept using some problems, using calculus.
Derivation of electric potentianl energy between two point charges using work-energy theorem. Electric potential energy of system of charges. Elecric potential energy or self energy of continuous charged bodies. Some typical problems relating work energy theorem.
Dfinition of electic potential due to a point charge. Calculation of electric potential at a point in space using principle of superpositon for descrete distribution and continuous distribution of chages.
Continuous Distribution of charges. (Uniform distribution of chages )
The relationship between change in electric potential energy and electric potential. Some problems on the path independency of change in potential energy.
Equipotential surfaces, the relationship betweeen jumping from one equipotential surface to other and electric field. Rough mathematical derivation beween electric field and electric potential. DIFFERENTIAL relationship between and V using (nabla)
Some problems on euipotential surfaces and electric field.
Definition and properties of an electric dipole, calculation of net dipole moment i.e vector addition of dipole moments, electric potential at a point in space due to a dipole. The change in position vector i.e. along and along . Derivation of electric field at a point in space using differential relationship betweeen and V, along directions and . Effects on a electric dipole placed in a uniform electric field, the net torque acting on a dipole due to external electric field, potential energy of a dipole in an external electric field. Net force and torque acting on an electric dipole placed in non uniform external electric field.
Electric field line, definiton and properties. Area vector, flux , elecrtic flux. Gauss law, some problems on direct gauss law, Gauss’ law and Coulomb’s law similarities.calculation of electric flux passing through a surface for different geometrical symmetries.
Application of Gauss’ law.
Discussion of properties of a charged conductor. Calculation of electric field due to a hollow sphere and drawing properties of spherical distribution, calculation of electric field due to a charged solid sphere, calculation of electric field due to infinite charge distribution i.e cylindrical symmetry, planar symmetry. Calculation of electric field inside a cavity. Application of above mentioned derivations for different geometrical arrangements.
Definition of a capacitor, geometrical, and theoretical (capacitance, potential drop, charge) parameters of a capacitor. Different types of capacitors depending on their geometrical arrangements, and calculation of their capacitance. The idea of polarization, permittivity constant of space, Coulomb’s law and Gauss’ law revised. Calculation of capacitance of a capacitor including the concept of permittivity of space. Circuits of capacitors, calculation of equivalent capacitance for an arrangement of capacitors. Energy stored in the capacitors.
1 D 2 B 3 B 4 B 5 D 6 B 7 A 8 B 9 D 10 A
read less
Answered on 17 Jun CBSE/Class 11/Science/Physics IIT JEE/IIT - JEE Mains/Physics/Physics and Measurement Tuition/BTech Tuition/Engineering Physics
Most of us would understand the concept of torque. However, I am going to ask a question which is slightly more involved.
I shall spin a rod of length 'L' with an angular velocity 'ω' about its centre of mass and place it on a ground with a kinetic friction coeficcient of η_{k}. Without using the torque equation and only applying Newton's 2^{nd} law of motion (F=ma) , could you derive the rod's 'ω' as function of time, 't'.
This is a very interesting exercise to clearly understanding the various forces acting on and inside a rigid body, the direction of those forces and the associated unknowns.
Many students fail to understand the constraints of a rigid body motion. They also do not easily appreciate how using the torque euqation so much simplifies rigid body dynamics.
I hope this exercise will be fun. I will post the solution in a few days though.
read lessKashish Solanki
Tutor
Most of us would understand the concept of torque. However, I am going to ask a question which is slightly more involved.
I shall spin a rod of length 'L' with an angular velocity 'ω' about its centre of mass and place it on a ground with a kinetic friction coeficcient of η_{k}. Without using the torque equation and only applying Newton's 2^{nd} law of motion (F=ma) , could you derive the rod's 'ω' as function of time, 't'.
This is a very interesting exercise to clearly understanding the various forces acting on and inside a rigid body, the direction of those forces and the associated unknowns.
Many students fail to understand the constraints of a rigid body motion. They also do not easily appreciate how using the torque euqation so much simplifies rigid body dynamics.
I hope this exercise will be fun. I will post the solution in a few days though.
Asked on 09 Jun CBSE/Class 11/Science/Physics IIT JEE/IIT - JEE Mains/Physics/Physics and Measurement Tuition/BTech Tuition/Engineering Physics
Most of us would understand the concept of torque. However, I am going to ask a question which is slightly more involved.
I shall spin a rod of length 'L' with an angular velocity 'ω' about its centre of mass and place it on a ground with a kinetic friction coeficcient of η_{k}. Without using the torque equation and only applying Newton's 2^{nd} law of motion (F=ma) , could you derive the rod's 'ω' as function of time, 't'.
This is a very interesting exercise to clearly understanding the various forces acting on and inside a rigid body, the direction of those forces and the associated unknowns.
Many students fail to understand the constraints of a rigid body motion. They also do not easily appreciate how using the torque euqation so much simplifies rigid body dynamics.
I hope this exercise will be fun. I will post the solution in a few days though.
read lessLesson Posted on 04 Jun CBSE/Class 10/Mathematics IIT JEE/IIT - JEE Advanced/Mathematics/Integral calculus IIT JEE/IIT - JEE Mains/Mathematics/Integral Calculus
Indrajit
I am successfully providing tuition of Mathematics in Class IX-XII of all Boards near Kavi Najrul Metro...
Before starting the discussion I would like to mention this problem
The conventional way to solve this problem is to deal with trigonometric identities and to mange by parts, but this type of problem can be easily solved by applying results of Beta and Gamma Functions.
———————————————————————————————————————————————————
Gamma Function:
The gamma function denoted by is defined for positive values of by the integral
.......(1)
Now,
1. For any
2.
Integration by parts gives
As and , the integreted part vanishes at both limits and therefore,
i.e.
3.
By direct computation converges
4.
Combining the above reletions,
Beta Function:
The beta function denoted by is defined for positive values of m and n by the integral
1.
This reletion can be established by giving the transformation
2.
Substituting
,then
Now letting , we have
also,
.
3.
This reletion can be established by by giving the transformation in the definition of Beta Function.
4.
This can be established by putting
in
5.
so,
—————————————————————————————————————————————————————
Now Lets solve the problem:
Now to solve this problem plug
in
=
As
read less
Lesson Posted on 30 May IIT JEE/IIT - JEE Mains/Mathematics/Sequences and Series CBSE/Class 10/Mathematics/UNIT II: Algebra/Arithmetic Progression
Hemant P.
1. I have taught at various prestigious institutes of repute in India and abroad. 2. Worked at (i)...
Sequences
Mathematics is the science of patterns and homogeneity. Sequences are all about them.
A sequence has a traditional meaning in mathematics similar to that in ordinary language.
A sequence is any regular pattern exhibiting some characteristic property throughout.
To be precise, any sequence is characterised by a property.
Let us take a simple example of a common most sequence of all, the series of natural numbers, 1, 2, 3 …n. This sequence is characterised by a property that every term is one more than the previous term. Therefore, the sequence is bounded by a property. We may find an infinite number of sequences. You may note that to generate a sequence we need two things. We begin with a starting term, and a rule defined to get the next term or a general term. This general term is often called generating term.
There are of course sequences that are unbounded and may run infinitely on either side. These may be termed as infinite sequences. The series, which we are dealing with, are called finite sequences, for the apparent reason that they are bounded, i.e. they have the last term. The other types of sequences are called infinite series, which we would take afterwards.
We are now in a position to define a sequence, a finite series. We start with the bound of a series. The bound of a series are the values which the terms or members of a sequence can take. You may understand them as the limits of the series. For example, if we have specified that write all natural numbers less than 10, then we have clarified that our sequence has a limit of n varying from 1 to 9 since we have to find all natural numbers less than 10. A series may be generated by a rule alone along with the set or bound in which it is defined. We call this generating term as the general term of a sequence. You may now guess the general or generate the name of our series of natural numbers. Yes, it would be
tn=n; here tn is the symbol of the general term. A sequence is, therefore, a function of a general term. For each value of n, we get a particular term of the series. We are now in a position to define few finite sequences ourselves.
We start with a general term tn = 2n+1 ;
0 < n < 10
You can yourself get few values by putting n = 1, 2, 3 etc.
t1 = 2⋅1+1 = 3
t2 = 2⋅2+1 = 5
and t3 = 2⋅3+1 = 7 etc.
Note that this sequence is a contiguous finite sequence hence we would substitute only values in the range of 0 < n < 10; i.e. we have just nine terms in the series.
Till now we have an idea of a finite sequence. Discussion done till now summarises that a finite sequence has following properties.
Starting term or the initial term
The generating term or general term or the rule to get the next term
Please note that a finite sequence is always bounded, but the reverse is not always true. There may be a sequence which is bounded but may not be finite. Consider the sequence 1,.1,.01,.001… .Here the general term is given by tn =. You can see that all the values of this sequence lie in the range 0 and 1 (This sequence is a continuously decreasing sequence, and it will never reach zero as exponent are always positive, but they can reach as near to zero as possible. We call this phenomenon as converging which you will learn in higher grades). Hence this sequence is bounded in the semi-open set (0, 1], i.e. greater than zero and less than or equal to 1.
Let us take a few examples of finite sequences with general term given. You are required to find the first few terms.
tn = 3n+1 ; 0 < n < 3
tn= 2^{n}-1 ; 0 < n < 13
Note that n can only take the value of positive integers, although it may have range.
You can quickly get terms of the sequences defined above, by putting the values of
n = 1, 2, 3, etc. You can check your answers from these:
The sequence is 4, 7, 10
The sequence is 1, 3, 7 … ,
Find more notes here.
read less
Lesson Posted on 04 Apr CBSE/Class 11/Science/Physics IIT JEE/IIT - JEE Mains/Physics/Physics and Measurement IIT JEE/IIT - JEE Advanced/Physics/Modern Physics
Vishesh Nigam
I am a Chemical Engineer and Khan Academy Talent Hunt Finalist (2017)(please watch my winning video below...
Lesson Posted on 01 Apr IIT JEE/IIT - JEE Mains/Physics/Physics and Measurement Tuition/BSc Tuition/BSc Physics CBSE/Class 11/Science/Physics
Why Electric and Magnetic Field lines can not intersects??
Sandip Mandal
since tangent at any point on the field lines gives the direction of field(electric or magnetic field) so if two field lines intersects then at the intersection point we can draw two tangents from one point which is never possible since at any point only one tangent can be drawn.
read less
Lesson Posted on 27 Mar Oscillations Waves IIT JEE/IIT - JEE Mains/Physics/Oscillations and Waves Electromagnetic Induction and Alternating Currents
PERIODIC MOTION AND OSCILLATORY MOTION
Kumar Kumar Sir
Earlier working with FIITJEE and Aakash about 18 years and now running an institute in The name of Kumar...
When a body repeats its motion along a definite path after regular interval of time, its motion is said to be periodic motion and interval of time is called time period (T). The path of periodic motion may be linear, circular, elliptical or any other curve. For example, the revolution of the earth about the sun.
To and fro type of motion is called an oscillatory motion. It needs to periodic and has fixed extreme positions. For example, the motion of pendulum of a wall clock.
The force/torque directed towards equilibrium point acting in oscillatory motion is called restoring force/torque.
If the restoring force/torque acting on the body in oscillatory motion is directly proportional to the displacement of body and is always directed towards equilibrium position, then the motion is called simple harmonic motion (SHM). It is the simplest form of oscillatory motion.
Lesson Posted on 27 Mar IIT JEE/IIT - JEE Mains/Physics/Oscillations and Waves Electromagnetic Induction and Alternating Currents IIT JEE/IIT - JEE Mains/Physics/Physics and Measurement
Mechanical Wave (Medium is essential)
Kumar Kumar Sir
Earlier working with FIITJEE and Aakash about 18 years and now running an institute in The name of Kumar...
Method of energy propagation, in which disturbance propagates with definite velocity without changing its form, is called a mechanical wave.
Energy and momentum propagate by the motion of particles of a medium. But medium remains at the previous position; the mass transfer does not take place.
Propagation is possible due to the property of medium viz. elasticity and inertia. Mechanical waves may be of two types :
UrbanPro.com helps you to connect with the best in India. Post Your Requirement today and get connected.
Ask a Question