# Energy of Magnetic field by current in a long bar

Obviously, the energy density is proportional to the square of B, which is proportional to 1/r (radius).

Thus, the EM energy as the space integral of the energy density is infinite.

This would suggest that a current through a very long bar cannot be realized. May I understand such a result as that current flowing through a very long bar can not be truely realized without a returning line for forming a loop?