Question

State and explain amperes circuital law

Answer 1

Step 1. State Amperes circuit law

Ampere's circuit law state that the line integral of the magnetic field r around a closed path is equal to the product of magnetic permeability of that space and the current through the area bounded by the path .

That is $\oint B·dL={\mu }_{0}I$

Where $B$ is the magnetic field , ${\mu }_0$ the magnetic permeability and $I$ is the current through the area bounded by the path .

Step 2. Explanation

1. Ampere's circuit law is the generalization of Biot-Savart's law.
2. It is used to determine the magnetic field at any point due to distribution of current

Let us find the magnetic field at a point due top long straight wire carrying current

L Let imagine a Ampereian loop of radius $r$ which is circular and the wire carrying current pass through its centre $P$

$$\begin{gathered} \therefore \oint B·dL={\mu }_{0}I \\ \Rightarrow B\oint dL={\mu }_{0}I \\ \Rightarrow B·2\pi r={\mu }_{0}I \\ \Rightarrow B=\frac{{\mu }_{0}I}{2\pi r} \\ \Rightarrow B=\frac{{\mu }_0}{4\pi }·\frac{2I}{r} \end{gathered}$$