State and prove ampere's circutal law.
Answers
Ampere's Circuital Law states the relationship between the current and the magnetic field created by it. This law states that the integral of magnetic field density (B) along an imaginary closed path is equal to the product of current enclosed by the path and permeability of the medium.
ANSWER
Ampere's law states that the line integral of magnetic field 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.
∫
B
.
dl
=μ
0
I
One simple application of this law will make you understand it better.
We'll find the magnetic field at a point due to a long straight current carrying conductor.
For this we imagine an Ampereian loop which is circular with the centre at the wire and passing through the point P.
∫
B
.
dl
=μ
0
I
Since the path is a circle, the magnetic field intensity
B
is uniform throughout because every point is equidistant.
μ
0
I=B.∫dl=2πr
∴B=
2πr
μ
0
I
=
4π
μ
0
r
2I
In SI units, value of
4π
μ
0
=10
−7
, it'll be easier to calculate in that form.