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/� 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 2pr. 

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/� dl = I 

Since, �B� is constant,

                                                          B?dl=I�.

�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 = I�.N

                                                       B = I�.N/L = I�.n            

n is the number of turns per length.

Entry # 10

By Zohaib Tariq