Ampere's Law

Ampere’s Law

“ If a circular loop is drawn around a current carrying conductor; it will erect a magnetic field ‘ B ’ around it, then to free space”

                                                             ∮B/μ dl = I

Where, ∮ is the integral representation of the total area of magnetic field ‘B’ of the circular loop of current carrying conductor.

In case of Straight Wire:
                                                  

Since, “B” (the red dots) is uniform, it behave as a constant value (as amount of current is same in conductor). Now ‘dl’ is a small part of the total circular loop, for which we have to find the value of ‘B’ at that point. Now, as ‘dl’ is small area of the circle, or we can say it’s a derivative of the total area bounded by the circular loop (circumference of the circular loop), so, if we take an integral of “dl” we can have the total area bounded by the circular loop which is 2πr. 

In case of Solenoid:

Here, the solenoid has number of turns “N” and is having a length “M”. where, “dl” is the small part of the circular solenoid. “B” magnetic field is also constant throughout the region because the amount of current Is same in the solenoid.

So,

                                                         ∮B/μ dl = I 

Since, ‘B’ is constant,

                                                          B∮dl=Iμ.

“dl” is a small part of the solenoid of having a Length “M” so the integral of “dl” would be the total length of the Solenoid. And it is having the Number of turn 'N'

                                                           BL = Iμ.N

                                                       B = Iμ.N/L = Iμ.n            

n is the number of turns per length.

Entry # 10

By Zohaib Tariq