. T ORQUE ON C URRENT L OOP , M AGNETIC D IPOLE . . Torque on a rectangular current loop in a uniform magnetic field We now show that a rectangular loop carrying a steady current I and placed in a uniform magnetic field experiences a torque.
It does not experience a net force. This behaviour is analogous to that of electric dipole in a uniform electric field (Section . ). We first consider the simple case when the rectangular loop is placed such that the uniform magnetic field B is in the plane of the loop.
This is illustrated in Fig. . (a). The field exerts no force on the two arms AD and BC of the loop.
It is perpendicular to the arm AB of the loop and exerts a force F on it which is directed into the plane of the loop. Its magnitude is, F = I b B Similarly it exerts a force F on the arm CD and F is directed out of the plane of the paper. F = I b B = F Thus, the net force on the loop is zero . There is a torque on the loop due to the pair of forces F and F .
Figure . (b) shows a view of the loop from the AD end. It shows that the torque on the loop tends to rotate it anti-clockwise. This torque is (in magnitude), a a F F τ = ( a a IbB IbB I ab B = I A B ( .
) where A = ab is the area of the rectangle. We next consider the case when the plane of the loop, is not along the magnetic field, but makes an angle with it. We take the angle between the field and the normal to FIGURE . (a) A rectangular current-carrying coil in uniform magnetic field.
The magnetic moment m points downwards. The torque τ is along the axis and tends to rotate the coil anticlockwise. (b) The couple acting on the coil. the coil to be