Question

State Ampere’s circuital law.

Answer 1

Hint:
Ampere’s circuital law is one of the most important laws in the domain of electromagnetism. Ampere’s circuital law gives the relationship between the current magnetic field created by the current and the path through which the current is flowing. Using this relationship mentioned before, state Ampere’s circuital law.

Complete answer:
The statement for Ampere’s circuital law is given as:
The line integral of magnetic field strength $\vec { H }$ around a single closed path is equal to the total current enclosed in that path. Mathematically, it is given by,
$\oint { \vec { H } . d\vec { l } }= I $ ...(1)
Where, H is the magnetic field strength
            dl is the length element of path
            I is the total current
We know, $H=\dfrac { B }{ { \mu }_{ 0 } }$ …(2)
Where, B is the magnetic field induction
            ${\mu}_{0}$ is the permeability of free space
Substituting equation. (2) in equation. (1) we get,
$\oint { \vec { \cfrac { B }{ { \mu }_{ 0 } } } . d\vec { l } } = I$
$\Rightarrow \oint { \vec { B } . d\vec { l } } = { \mu }_{ 0 }I$
Thus, we can also state Ampere’s circuital law as:
The line integral of the magnetic field induction $\vec {B}$ around a single closed path is equal to the absolute permeability of free space ${\mu}_{0}$ times the total current enclosed in that path.

Note:
Students must not confuse between Ampere’s circuital law and Ampere’s work law. Both the laws are the same. Ampere’s law is a generalization of the Biot-Savart’s law and is used to determine magnetic field at any point due to distribution of current. Ampere’s circuital law plays the same role in the magnetic field as Gauss law plays in electrostatic physics.