Question

Using Ampere circuital law, obtain an expression for magnetic field ‘B’ at a point at a perpendicular distance ‘r’ from a long current carrying conductor.

Answer 1

By Ampere Circuital law,

`oint vecB * vec(dl)` = μ₀I

Since `vecB || vec(dl)`, θ = 0° ⇒ cos θ = 1

`oint B d l cos theta` = μ₀I

`oint B d l` = μ₀I

`B oint d l` = μ₀I

B (2π r) = μ₀I

B = `(mu_0 I)/(2 pi r)`