4.7 Ampere's Circuital Law

Subject: Physics

Class XII

Chapter: 4. Moving Charges and Magnetism

Ampere's Law

 "The integral of magnetic field around a closed path is equal to the product of absolute permeability and total current passing through it."

Mathematical form

∮B.dl = μ₀.I

Here,

B = Magnetic field

dl = Current element

μ₀ = Absolute Permeability

I = Current passing through it

Proof

Consider about an infinitesimal carrying conductor through which I current passing is passing. Magnetic field lines are produced around the conductor as the form of concentric circles.

Magnetic field at a distance due to this infinitesimal conductor. 

B = μ₀.2I/4πa ................... (i)

Now consider about a circle of radius a having a current element dl.

Both B and dl have same direction because B is along the the tangent of circle.

Hence,

B.dl = Bdlcosθ = Bdlcos0⁰ = Bdl

Now integrate the closed path

∮B.dl = ∮Bdl .............. (ii)

Now putting the value of B

∮B.dl = ∮μ₀.2Idl/4πa

∮B.dl  = μ₀.2I/4πa∮dl

For complete cirecle

∮dl = 2πa

∮B.dl  = μ₀.2I.2πa/4πa

∮B.dl = μ₀.I

Proved