Problem $2$

Understanding the magnetic field distribution around current$-$carrying conductors is essential for designing effective electromagnetic interference shielding, particularly in high$-$frequency transmission line circuits, where controlling electromagnetic coupling is critical for maintaining signal integrity. In this context, consider such a scenario that direct current I flows in a straight wire of length $2L$ along the $z-$axis,

$($a$)$ can you create a sketch and explain to your tutor how you would approach solving part $($b$)$ the problem?

$($b$)$ find the magnetic flux density $B$ at a point located at a distance $r$ from the wire in the bisecting plane by determining the vector magnetic potential $A.$

$[$Hint: You have already solved the similar problem by using Biot$-$Savart Law in week $5.$ Now, you are asked to solve the problem by using vector magnetic potential : $)]$