derivation for ampere circuital law - Physics - Current Electricity

Question

derivation for ampere circuital law?

Hansraj Rai · Accepted Answer

Dear Student!! Proof of Ampere's circuital law:

Consider along straight conductor carrying current I The magnetic induction B at a distance r from the conductor is given by , $B = \frac{μ_{0} I}{2 π r}$ the direction of B vector is along a tangent to the circle of radius r Now, $\oint \vec{B} \vec{d l} = \oint B d l \cos 0^{0} = \oint B d l = B \oint d l = B (2 π r) = \frac{μ_{0} I}{2 π r} \times (2 π r) = μ_{0} I$ which is Ampere circuital law