Answer 1

Magnetic field due to straight infinite current carrying wire:

The figure below shows a straight infinite current carrying wire around which a circular loop of radius r is shown

The field lines are circular, and hence, the field B at any point of the circular loop is directed along the tangent to the circle at that point. The magnitude of field B is the same at every point of the circular loop.

Therefore, we get

∫B.dl=∫Bdl cosθ = ∫Bdl cos0 = B∫dl =B(2πr)

Now, from Ampere’s circuital law, the above equation is

`B(2pir)=mu_0I`

`:.B=(mu_0I)/(2pir)`