Question

plz explain this question​

Answer 1

Magnetic field intensity at the centre of the coil shall be contributed bhai that coil as well as the infinite wire.

Using right hand thumb rule we can determine the direction of magnetic field intensity due to the coil as well as the infinite wire. We can see , that the net magnetic field intensity will be out of the plane of the paper.

Calculation :

Magnetic Field Intensity due to coil at the centre will be :

$B1 = \dfrac{ \mu}{4\pi} \bigg \{ \dfrac{i}{r} \times 2\pi \bigg \} \: \hat k$

Magnetic Field intensity due to infinite wire at the centre of coil will be

$B2 = \dfrac{ \mu}{4\pi} \bigg \{ \dfrac{2i}{r} \bigg \} \: \hat k$

So net Magnetic Field intensity will be :

$B_{net} = B1 + B2$

$= > B_{net} = \bigg \{ \dfrac{ \mu}{4\pi} \bigg(\dfrac{i}{r} \times 2\pi \bigg ) + \dfrac{ \mu}{4\pi} \bigg (\dfrac{2i}{r} \bigg ) \bigg \} \hat k$

$= > B_{net} = \bigg \{ \dfrac{ \mu i}{2\pi r} \bigg( 1 + \pi \bigg ) \bigg \} \: \hat k$

So final answer :

$\boxed{ \red{ \bold{ B_{net} = \bigg \{ \dfrac{ \mu i}{2\pi r} \bigg( 1 + \pi \bigg ) \bigg \} \: \hat k}}}$