The responses of a current-carrying coil to an external magnetic field is identical to that of a magnetic dipole (or a bar magnet). Like a magnetic dipole, a current-carrying coil placed in a magnetic field \(\vec B\) experiences a torque. In that sense, the coil is said to be a magnetic dipole. To account for a torque τ on the coil due to the magnetic field, we assign a magnetic dipole moment \(\vec \mu\) to the coil, such that
\(\vec {\tau}\) = \(\vec \mu\) x \(\vec B\) = NI\(\vec A\) x \(\vec B\)
where \(\vec \mu\) = NI\(\vec A\). Here, N is the number of turns in the coil, I is the current through the coil and A is the area enclosed by each turn of the coil. The direction of \(\vec \mu\) is that of the area vector \(\vec A\), given by a right hand rule shown in below figure. If the fingers of right hand are curled in the direction of current in the loop, the outstretched thumb is the direction of \(\vec A\) and \(\vec \mu\). In magnitude, μ = NIA.
The torque tends to align \(\vec \mu\) along \(\vec B\).
