Biot Savart's law ant its expression

“Biot - savart's law”:
Scientist biot and savart deduce an expression for the intensity of magnetic field due to a current carrying conductor which is known as biot savart law.

Let xy be a conductor, carrying current I ampere. Consider a small line element dl of this conductor. This small element is also called as current element.
The intensity of magnetic field (dB) at a point P due to this current element is -

1) Directly proportional to the current
      i.e      dB ∝ I

2) Directly proportional to the length of current element
      i.e      dB ∝ dl

3) Directly proportional to the sinθ
Where  is the angle between current element and position vector of observation
      i.e.      dB ∝ sinθ

4) Inversely proportional to the square of distance between the observation point and current element
       i.e.      dB ∝ 1/r²

Combining above relations -
       dB ∝  (I.dl.sinθ )/r²

       dB =  K.(I.dl.sinθ )/r² --------(1)

Here, K = Proportionality constant

⇒ In CGS System for air/vacuum
     K = 1 then from enq(1)

   [  dB = (I.dl.sinθ )/r² ]  oersted or gauss

⇒ In SI unit for air/vacuum

K = μo/4π  =  10^-7  N/A²
Where μo = Permeability of free space
From eqn(1) -

 [ dB = μo/4π ×  (I.dl.sinθ )/r² ] tesla or       
                                                       N/(A×m)
This is “Biot Savart's law”


# DEFINATION OF “ELECTRO-MAGNETIC UNIT” OF CURRENT ( CGS unit of current)

We know that by Biot Savart's law”

dB = (I.dl.sinθ )/r²  oersted or gauss

Here putting, I = 1 emu , dl = 1cm, θ = 90°
And r = 1cm
Then,  dB = 1×1×sin90 / 1²
            dB = 1 gauss

* Definition : one emu of current is that current which produce a field of 1 gauss, at the center of conductor of length 1cm, placed in the form of an arc of a circle of radius 1cm.

# DEFINITION OF “ONE AMPERE” BY BIOT SAVART'S LAW

We know that

dB = μo/4π ×  (I.dl.sinθ )/r²  tesla

Here putting  μo/4π = 10^-7  N/A²
I = 1 ampere, dl = 1m ,  θ = 90° and r = 1m

dB = 10^-7×1×1×sin90° / 1²

dB = 10^-7 tesla

* Definition : The practical unit of current is ampere. one ampere of current is that current which produce a field of 10^-7 tesla, at the center of conductor of length 1m, placed in the form of an arc of a circle of radius 1m.