where V here represents volume. 

3.1 Find the vector potential of an infinite solenoid with n turns per unit length, radius R, and current I.

3.2 What current density will produce the vector potential \(A\ =\ k\hat{\phi}\) in cylindrical coordinates?

4. Magnetic Force

In the presence of both electric and magnetic fields, the force (also known as Lorentz's Force) acting on a charged particle is given by: