Gauss's Law: definition, explanation, formula

Definition:

"Gauss's Law states that, Electric flux around a closed surface is depends upon charged enclosed in that surface and permittivity of free space."

Explanation:

Gauss's law states tell us about electric flux through some closed surface or area,
Electric flux through some area depends upon the charge enclosed by that area and the permittivity of free space in that area.
consider there is a closed sphere and there is charge enclosed in it, the flux out of it or the electric field out of the whole area could be determined with the help of Gauss's law.

Consider we wan to find the electric flux through the green planer area, then it will be simple that electric field lines multiplied by area perpendicular to the lines.

But when there comes a closed surface then there is nothing best except Gauss's law to find electric flux through closed surface (enclosed charge.)

It is not necessary that the surface should be closed sphere it could be any type of closed surface. And we will use Gauss's law to determine the electric flux through it.

Formula:

Mathematically we can determine the electric flux through closed surface by formula,

Where Q is the amount of charge enclosed and Ɛ is the permittivity of free space and 𝛟 is electric flux through the surface.

Electric Charge density, definition, explanation

Definition:

"Electric charge density is the amount of charge on unit volume space or surface or area."

Explanation:

Electric charge density is the density of charge on unit area, the charge could be less or  more, and charge could be positive or negative.
as shown in figure 1 below, in which there is positive charge on surface but less and on figure 2, there is more positive charge.

So area in figure 2 have more electric charge density than figure 1.

The area or volume could be one dimensional, two dimensional and three dimensional. 

Formula:

The electric charge density can be written in the form,

Where p is the charge density and q is the amount of charge and v is the volume of space and unit area. we can replace the v by A, when there is unit area.

Electric flux density, definition, explanation

Definition:

"Electric flux density is the electric flux passing through some unit area, and its direction is perpendicular to that unit area."

Explanation:

"Electric flux density", when we break down this sentence into "electric flux" and "density".
Then it is easy to understand that, the density of electric flux across some area. Consider there is a unit area shown below.

Electric flux is passing through this, in direction perpendicular to the unit area. The amount of electric flux passing through this unit area, in direction perpendicular to the unit area is called Electric flux density.

Formula:

When we write mathematically the electric flux density it is equal to the product of electric field E and permittivity of material.

                                                                           D=Ɛ.E

Unit:

The unit of electric flux density is coulombs per meter squared. 

Coulomb's law, definition explanation

Definition:-

"The magnitude of electrostatic force of attraction and the magnitude of electrostatic force of repulsion between two point charges is directly proportional to the product of magnitude of both charges and inversely proportional to the square of distance between them(both charges)."

Formula:-

mathematically we can write this in the form,

where F is the force,

q1 is the charge 1 and q2 is the charge 2,

and r is the distance between them.

this proportionality can be removed by placing proportionality constant k. in the formula, 

where the value of this constant depends upon the medium between the two point charges.

When there will be air then its value will be 9.0 x 109 N • m2 / C2.

And this value of k will change, with the change in medium between the two charges.

Lenz's law, definition, explanation

Definition:-

"The electric current induced in a circuit or somewhere, always tries to decrease the source which produces it or flow in opposite direction to decrease its effect."  

Lenz's law expand the law of electromagnetism which only tell about induced electric current.

Explanation:-

As we came to know through Lenz's law that the current induced, always tries to do opposite, for the source which is producing it, 

Example:-

lets take an example of a permanent magnet and a coil. 

When we bring the magnet north pole near to the coil there will be change in magnetic field across coil as we move magnet, thus because of changing magnetic field there will induce electric current in it. As we bought the north pole of magnet to the coil, so current induced in coil will start to flow in such a direction that it will make north pole of it towards the permanent magnet north pole, as everybody knows that, like poles of magnet repel each other, hence there, these two north pole will also follow the same rule. And When we will try to bring back the magnet then the current induced in the coil will flow in such a direction, that it will make south pole towards the permanent magnet north pole, where unlike poles attract each other, hence they will attract each other. 

So by doing this current induced in the coil is trying to oppose the source(permanent magnet). By pushing it back when we bring near it(creating north pole towards north pole of magnet) and by pushing it closer when we bring back the magnet(by creating south pole towards the magnet.)

Faraday'laws of electromagnetic induction

Faraday's have proposed 2 main Laws,
Faraday's law of electromagnetic induction is also known as law of electromagnetism.

Faraday's first law:-

This law is the base of electric generators and motors.

Faraday's law stated that,
"When ever we place a conductor in a magnetic field which is varying with time then there will induced current in the conductor."
And if conductor is connected to a closed circuit then this current will flow through it.

Explanation:-

If a conductor is placed in a field of magnet, if both conductor and magnet are stationary then there will no induced emf in it. But when we will move magnet away from the conductor then magnetic field will change through conductor and then EMF(electromotive force) will induced in conductor. Even if we keep magnet stationary and move conductor then also emf will induced.

Faraday's Second law:-

We use this law often,

"The EMF induced in a coil is equal to the change of flux(by a magnet or something other) with the time. "

Where E is the induced EMF, and N is the number of turns of coil phi is the flux and t is the time.

Explanation:-

When a current is flowing through the coil then there is flux around the coil, when current will change then flux will also changes. And then EMF will induce in a coil.

The induced EMF could increase by:

1.By increasing the number of turns of coil.

2. By increasing rate of changing flux. by changing current rapidly.

3. By using good core on which coil is wound.

Self Induction, definition explanation formula unit

Self Inductance:-

"Self inductance is the property of coil to oppose change in current flowing through it"

Explanation:-

Consider there is a coil wire and current is flowing through it, whenever the current will change flowing through it, then there will induced emf which is known as self induced emf. And its direction will be opposite to the the current flowing through it. If current is increasing then self induced emf will try to decrease or flow in direction opposite to the current. But if current through the coil is decreasing then the induced emf will try to increase this current or will go in same direction as current is flowing.

In other simple words, Self induce emf will try to oppose in change in current.

This phenomena is known as Self induction.

Formula:-

The formula for self induction could be derive from the formula of induced emf formula.

Where L is the self induction, E is the induced emf and di/dt is the rate of changing current.

From this it is clear that self induction will increase when induced emf will increase and will decrease when rate of changing current will increase.

Unit:- 

Unit of self inductance is Henry(H).

"There will be 1 Henry of self inductance when induced voltage will be one and current will change 1 ampere in one second."

Capacitive and Inductive Reactance and their explanation

Capacitive Reactance:-

"Capacitive reactance is the resistance offer by capacitor to the current."

Explanation:-

Whenever there is current flows through the capacitor there is the opposition offer by it to the current, which causes delay in its charging. And its this reactance depends upon the frequency of AC current flowing through it. the more the frequency the less its reactance will be and less the frequency the more the reactance will be. The formula for the capacitive reactance is below.

Inductive Reactance:-

"Inductive reactance is the resistance offer by inductor to the current flowing through it."

Explanation:-

When AC current flows through the inductor it offer some resistance to the current. it depends upon the frequency of current. The more the frequency the more the reactance and less the frequency less the reactance. This behaviour is of inductor when AC current flows through it.

Inductor, Inductance, explanation, formula

Definition:-

"Inductor is an electronic device that is use to store energy in the form of magnetic field."

Explanation:-

Inductor store energy in magnetic field around it. Inductor is an coil of a conductor(wire). wire wounding on some rod or magnet. when a current passes through the conductor then there will be magnetic field around the wire. We wound the wire because by winding there would produce a strong magnetic field around this, we could increase the strength of  magnetic field around coil by taking efficient core like magnet and by increasing number of turns of coil and increasing cross sectional area of inductor. When current flows through the inductor there would produce magnetic field around it and in that magnetic field energy would be store (in the form electrons). It would be store until current is flowing through it. When current will stop it will release all the energy.

Inductor does not allow AC current to flow through it due its changing direction nature. While inductor resist to change in current so it becomes open in a circuit while AC current flows through the circuit. It allows DC current to flow through it. After charging completely it allows DC to flow through the circuit hence become short in circuit with zero resistance.

Inductance:-

Inductance is the property of a inductor which is that "whenever Flux is changed in it, it produces an EMF."

or in simple words

Inductance is the ability of an inductor to store energy in the form magnetic field.

Henry is the unit of Inductance.

Formula:

formula for inductance of inductor is,

Capacitor, definition, formula, explanation, Capacitance

Definition:-

"Capacitor is an electrical device which is used to store energy or charges between its plates."

Explanation:-

Capacitor is use to store charge so that we could use it later by discharging it. It stores electrical charge between its parallel plates which are known as conducting plates of capacitor. There is no connection between these conducting parallel plates. They are separated by air or some dielectric. We use dielectric in capacitor to increase its efficiency. By using dielectric we could store more charge between its plates.

Capacitor doesn't allow dc current to flow through it because DC current flows only in one direction. so, it after charging from dc current it allows to flow through it as there is nothing in the circuit.

While it allows AC current to flow through it because ac current changes its direction after half interval, so capacitor charges at first half and discharges at 2nd half.

Capacitance:-

Capacitance is the ability of a capacitor to store charge. Capacitance tells us that how much charge we can store between the plates of capacitor. Capacitance is the unit of capacitor in one way. While capacitance has unit Farad. Farad is define as,

"When there will be 1 volts across capacitor then it will charge one coulomb, its mean capacitor have one farad capacitance."

Formula:-

By seeing definition of farad we could write formula for the capacitance of capacitor,

Q = CV

C = Q/V

Power, its definition, explanation, formula, unit

Definition:-

"Power is define as rate of doing work or Work done per unit time."

Explanation:-

Power is the doing some work, taking less time. Power depends upon doing work and time taken to complete the work. A person have more power will do more work but take less time and person have less power will do less work but will take more time. So this is the concept of power. Work does not depend upon time while power depends upon. so this is the only difference between them.

Formula:-

The formula for power is work done per unit time.

Power = Work / time

as work is equal to 

work = F.d

so power would have,

Power = Force.displacement / time

P = F.d / t

Unit:-

Unit of power Watt  is define as " If one joule of work is done in one second then power will be one watt"

P = F.d / t

Watt= Newton. meter / seconds

Watt = joule / second.

Why like charges repel each other and unlike charges attract each other?

Why like charges repel each other?

"Like charges repel each other because, it depends upon where the two charges have their electric field forces directed."

As positive charge have electric field lines going away from it and when two positive charge particles come near to each other there electric field lines tries to bend each other and their lines of forces are opposite in direction with respect to each other so both particles tries to send away to each other and hence in this way they repels each other.

Below diagram explain all the things which is described above.

Why unlike charges attract each other?

Like charges attract each other because their electric field lines are in the same direction in respective to each other, as we know Negative charge have electric field lines towards it(or coming to each other), and positive charge have away from it or going away from it. so when both comes near to each other, while negative charge tries to attract positive charge and positive charge tries to move towards negative each other.

Below picture explain all the phenomena describe above.

Electric Fields lines and Forces

Electric Fields:-

"Electric Fields are the area or space or region around a body or particle which is charged, in which area it effects(attracts or repel) on other body or particle which is charged."

Explanation:-

Consider their is a charged particle A, it has Electric fields lines, because it is charged. When a unit positive charge(small charge) will come into its field lines then it will feel some force, which is the effect of Charged particle A. It will repel the unit charge (as positive and positive repel each other).

The unit positive charge will only feel this force when it will come into the region where there is Electric field lines of Particle A.

In above diagram unit charge 1 will feel force as it is in the field region of charged particle A, but 2 will not feel any force as it is out of field lines of charged particle A. 

Electric Forces:-

"The force which charged unit positive charge feel when it is in the electric field lines of charged particle (A)."

Explanation:-

As Charged particle have electric field region where it exerts some force on some other charged particle (when it comes in the electric field of that charge). There are two type of forces which is exert by the charged particle in its field region. Attractive force and Repulsive force. Positive charge exert repulsive force on other positive charged while it exert attractive force on negative charge. In general there is attractive forces in opposite charges and there is repulsive force in between like charges.  

In below pic A is positive charge and it is repelling other positive charge.

In below pic, A is positive charge which is attracting negative charge.

Logic Gates, Symbol, Table, explanation, logic

The logic gates are used to build digital cir

cuits. In fact digital circuits are build by logic gates. They are the main parts of digital circuits. Most of the logic gates have two inputs and one output. They are use to do switching in circuits.

There are basics seven types of logic gates.
1. AND gate
2. OR gate
3. NAND gate
4. NOR gate
5. XOR gate
6. XNOR gate
7. NOT gate

Now below is the symbol, logic table and some explanation of all above listed logic gates.

AND gate:-

Symbol of AND gate is,

Truth table of AND gate is,

OR gate:-

Symbol of OR gate is,

Truth table of OR gate is,

NOT gate:-

Symbol of NOT gate is,

Truth table of NOT gate is,

NAND gate:-

Symbol of NAND gate is,

Truth Table of  NAND gate is,

NOR gate:-

Symbol of NOR gate is,

Truth table of NOR gate is,

XOR gate:-

Symbol of XOR gate is, 

Truth Table of XOR gate is,

X NOR gate:-

Symbol of X NOR gate is,

Truth table of X NOR gate is, 

Equations of Motion(and their derivation)

There are three equations of motion:-

Explanation:-

This equation is used to find the final velocity of a body or latest velocity of body or current velocity of body. This equation is known ass first equation of body.
Whenever a body starts to move it have some initial velocity and when after some interval of time t it have some change in velocity, after which its velocity becomes So above equation is for final velocity. Now see its derivation.
Change in velocity ∆v is equal to,

(2)

This is equation is used to find the distance covered by a body having initial velocity Vi and after time t.

Consider a car moving with initial velocity Vi and final velocity Vf, then it would have average velocity will be,

 

(3)

In this equation there is distance , acceleration, final velocity and initial velocity are related.

We could find one, if we know other.

According to first equation of motion,