Question

State and explain Ampere’s circuital law.

Answer 1

In this question, we will study about the ampere’s circuital law and try to explain it by its application. This will help us to get the answer. Further, we will study the basics of the magnetic field and the rules to find the direction of the magnetic field.

Formula use:
$\oint {B.dl = {\mu _0}I}$

Complete answer:
Ampere's circuital law states that the line integral of magnetic field represented by B, around a closed path is equal to the product of the magnetic permeability of that space and the total current through the area bounded by that path.
$\oint {B.dl = {\mu _0}I}$
To understand the Ampere’s circuital law, we can see the below application of this law:
Let us find the magnetic field at a point due to a long straight current carrying conductor.
Now, we imagine an Ampereian loop which is circular with the centre at the wire and passing through the point P, as shown in the figure.
$\oint {B.dl = {\mu _0}I}$
Since the path is a circle, the magnetic field intensity B is uniform throughout because every point is equidistant.
${\mu _0}I = B\int {dl} = 2\pi r$
$\Rightarrow B = \dfrac{{{\mu _0}I}}{{2\pi r}}$
$\therefore B = \dfrac{{{\mu _0}}}{{4\pi }}\dfrac{{2I}}{r}$
So, this makes it easy to understand the Ampere’s circuital law.

Additional information:
A magnetic field B can be defined as a vector field that tells the magnetic influence on moving electric charges, electric currents, and magnetized materials. Also, we should know that a charge that is moving in a magnetic field experiences a force that is perpendicular to its town velocity and to the magnetic field.
Fleming's left-hand rule is used to find the direction of magnetic force acting in electric motors. We know that an electric current and magnetic field exist in an electric motor, and these lead to the force that creates the motion.
So, the left hand rule is used here which gives the direction of magnetic force acting in the electric motor.
Fleming's right-hand rule is used to find the direction of induced current in an electric generator. As we know that in an electric generator, the motion and magnetic field exist and these lead to the production of an electric current in the generator.
So, the right hand rule is used here to find the direction of induced current in an electric generator.

Note:
Do remember that the Ampere’s circuital law is for a closed loop. Further, we need to notice the direction of the magnetic field i.e., whether the field is inward or outward. All the three fingers should be placed perpendicular to each other.