Meaning of the Ampere’s Circuital Law Equation:
A current carrying wire produces a magnetic field that circles around the wire and is proportional to the amount of current flowing through the conducting wire.
Being one of Maxwell’s equations, the Ampere’s circuital law describes a relationship between the current and the magnetic field it produces. It states that if we sum up the magnetic field at all points of an imaginary loop drawn around a current-carrying conductor, it turns out to be proportional to the current enclosed by that imaginary loop and is equal in magnitude to permeability in vacuum times the enclosed current. In order to understand this beautiful equation, let us go back to the basics :
If we just go back to our high school science, we recall that a current-carrying wire produces a magnetic field around it. The direction of this magnetic field can be obtained by using the right-hand thumb rule, i. e., when we align the thumb of our right hand in the direction of current flowing through a conductor, the curling of the fingers would indicate the direction of magnetic field lines. So, we know that the magnetic field is in the form of closed loops around a current-carrying conductor which either loop clockwise or anti-clockwise. So far, so good! But what about the magnitude of this magnetic field that the current has generated around the wire through which it is flowing. Well, the easiest way to determine it is by using Ampere’s circuital law.
Another aspect of this amazing law is that just as the role played by the Gauss’s law in electrostatics, the same is played in magnetostatics is played by the Ampere’s law. In the 1820s, Ampere first identified that all magnetic effects are caused by the charged particles in motion, i.e., current. However, it is surprising that even being of extremely small magnitudes as compared to the electric forces, the magnetic forces still get noticed around a current-carrying wire? Well, this is because of the reason that even though a huge amount of negative charges are flowing down the wire, an equal positive charge is already present in the wire. So all the electric effects are masked and the magnetic field stands alone.