AMPERE LAW

Ampere Law its Integral and Differential From

• Ampere Law

The Ampere law states that a magnetic field is generated around a conductor when current flow through it. The magnitude of generated magnetic field at a point is directly proportional to amount of current and inversely proportional to distance between point and straight current carrying conductor. 

• Diagram  

• Direction of Magnetic Field

The direction of magnetic field is given by right hand rule stated as
 Grasp the current carrying wire in your right hand in such a way that erect thumb is along the direction of current. The curled fingertips around the wire indicates the directions of magnetic field.

• Explanation

Consider a straight conductor through which current I flows. The magnetic field B is generated around it in the form of circles. The magnitude of magnetic field B is generated around it in the form of circles. The magnitude of magnetic field B depends upon current I and distance r between conductor and point P where we want to evaluate magnetic field.
                  B ∝ I
                    B  ∝ I \ r
Combining both experimental facts
                    B ∝ I \r
                    B = μ_{0  \ 2}π (I\r)
   Where μ_{0  \ 2}π is constant of proportionality and 
μ_{0  is called permeability of free space its value is 4} π 10^-7 Wb\A-m.