$($a$)$ Find the magnetic vec$(B)$ field due to a straight current $I^{\text{'}}$ of finite length from $-$L to $+$L using BiotSavart Law, $($b$)$ find the magnetic vec$(A)$ vector potential by using the definition. Finally, $($c$)$ prove the magnetic field vec$(B)=$grad$$vec$(A)[30$ pts $]$