What is Ampere's Circuital Law? (Class 12 Physics)

Ampere's Circuital Law states that: "The line integral of the magnetic field (B) around any closed loop (called an Amperian loop) in free space is equal to the absolute permeability of free space ($\mu_0$) multiplied by the total net current (I) enclosed by that loop."

Simplified meaning: If you draw an imaginary circle (loop) around a wire carrying electricity, the total magnetic power curling along that circle is directly proportional to the amount of electricity trapped inside the circle.

The law is expressed using integral calculus: $\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{enclosed}$

• $\oint$: Indicates integration over a closed loop path.
• B: The Magnetic Field vector.
• dl: A tiny length element of the imaginary loop.
• $\mu_0$: Permeability of free space (a constant: $4\pi \times 10^{-7}$ T·m/A).
• I: The total electric current passing through the area of the loop.

The most famous use of Ampere's law is finding the magnetic field inside a Solenoid (a long coil of wire). Instead of calculating the field of thousands of individual wire rings, we draw a rectangular Amperian loop half inside the coil. Using the formula, we easily derive the clean result: $B = \mu_0 n I$ (Where 'n' is the number of turns per unit length).