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.