Question: Define and explain Ampere's law?

AMPERE'S LAW

The sum of the quantities of dot product of  B and vector length ∆L (B. ∆L) for all path elements of complete Loop is equal to μ。times the current (I) flowing through the conductor enclosed by the loop.

N

Σ (B. ∆L)r = μ。I

r = 1

EXPLANATION

Consider a closed Circular Path shown around a current carrying wire. This closed path is referred as Amperean path. Divide this path into large no. of elements each of vector length ĀL for each element remains the same. The direction of B at each point is tangent to the curved path. Then

B11 Δ L = B Cos θ Δ L = B Δ L Cos θ

= B. Δ L ...(1)

Where B11  = B Cos θ = Component of B parallel to ΔL

Where θ is the angle between B and ΔL. The sum of all the quantities B. Al. for all path elements in a closed path is equal to μo times the current enclosed by the Loop It can be represented as

(B. ΔL)1 + (B. Δ L)2 + --------- + (B. Δ L)N = μ。I

In summation form,

N

Σ (Β. Δ L)r = μο1 ... (2)

r=1

This is known as Ampere's circuital law Aho is a constant known as permeability of free space. In SI units its value is

μο = 47 ⊼  ✕ 10-7 Wb A-1m-1

Where, N= Total no. of length elements in a closed loop.

r = Variable changes from 1 to N.