Ampere's law: explanation, definition, formula

Definition:-

"Ampere's Law states that magnetic field around a conductor in which electric current is flowing, is directly proportional to the amount of electric current flowing through conductor."

Explanation:

Ampere's law provide us method or formula to calculate magnetic field, produced by electric current.
Just like electric field is directly proportional to the amount of charge, the magnetic field is directly proportional to the amount of electric current from which it is producing.

Formula:-

The most difficult in ampere's law is to derive its equation or make the formula for calculating the magnetic field around a long conducting wire.
So let's start this,
Consider we have long straight conducting wire, when electric current flows through it, the magnetic fields produces around the wire in concentric circle. As shown in below pic.

Every circle is for some specific part of wire and as we move forward in wire, the distance between these circles increases, that mean magnetic field is decreasing. Direction of magnetic field can be found by Fleming's right hand rule.(with direction of current giving)
Now to make the formula, consider there all the parts of wire( which have there magnetic field circuit) having length L and there magnetic field around these parts or elements is B for (every part).

So the equation will become,

And after removing proportionality,

where 𝝁 is the premiability of material or conductor.
B is the magnetic field and delta L is the sum of all length parts and I is the current flowing through the conductor,
sigma shows that the sum of all the length elements or parts with their magnetic field.
Where delta L could be replace by 2πr for particular(single part) length element.
So Then magnetic filed would become,

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.

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.

Work

Definition:-

"Work is the product of force and the distance covered by a body due to force applied on it"

Explanation:-

In physics work is done on a body, when we apply some force on it and it covers some distance in the direction of force.

Work is not done until body is not covering some distance whether force is applied on it or not, body has to cover some distance in order to get work done. or work will not be done until force will not be apply on it whether it is covering some distance or not. so both things are necessary.

Example:-

1.When you try to push the box by applying force on it and box start to move in direction of force, then your are doing work.

2.When you try to push the wall then you apply force but wall doesn't move, so you are not working (According to physics).

Unit:-

The Sl unit of work is joule J

Formula:-

Work also have an formula to calculate it mathematically,

W=F.d.cosθ

As define work is the product of force and distance and the angle between them. 

Conditions:-

1.This cos shows that when force applied and distance covered is in same direction then angle will be 0, where cos(0)=1, hence work will be maximum.

2. When force applied and distance cover will be perpendicular to each other than angle will be 90 and cos(90)=0, hence work will be 0.

3. When force applied and distance covered is in opposite direction  then work will be negative as, angle will be 180 and cos(180)=  -1.

Centripetal force

Definition:

"Centripetal force is a force, which keeps a body moving in a circular path and that force acting towards the center of that circular path."

Explanation:

A body never automatically or itself moves in a circular path it, there is always a reason or some force that causes it to move in a circular path and that force in general is known as a centripetal force. and that force is always directed towards  center. it means force is from the center of circular path that causes it to move in a circular path.

Example:

You tries to move a string in a circular path. one end of it is in your hand and other is tied with a stone. and consider that stone is a body. you provide force from your hand which is at the center of circular path in which stone(body) is moving.

Formula:

 

This equation shows that force depends on the mass of body and the velocity by which it is moving in path and the distance(r) between the center of circular path and body.