Question

relationship between electric current and magnetic field

Answer 1

First of all @yahm : A Warm Welcome to 'Open Study'. Please Read CoC (compulsory to read by all "Open Study" users) : http://openstudy.com/code-of-conduct

Answer 2

current is rate of flow of charge. moving charges produces Magnetic field around them.
http://en.wikipedia.org/wiki/Maxwell's_equations#Conventional_formulation_in_SI_units
perhaps fourth equation is the one you want.
for a conductor just put \( \frac{\partial E}{\partial t} = 0\) you get the original one (Ampere cirtuital law)

Answer 3

Electric current applies a magnetic field around the wire, in the simplest form. I suggest you to look a physics II book for detailed information.

Answer 4

current carrying loop produce magnetic field