Torque on a Magnetic Dipole

If an electric dipole p is placed in a uniform electrostatic field E, it will experience a torque vector τ = p x E, but not translational force. Similar to it a magnetic dipole m experiences a torque vector τ = m x B, when placed in a magnetic field B. The torque is such that it tends to align the dipole with the field. The generalization to an arbitrary current loop is obtained by considering the loop as made up of a large number of infinitesimal square loops, each with a dipole moment dm. The torque on each square dipole is dm x B. Its integration over all the infinitesimal dipoles gives the relation for the total torque.

            τ = ∫ dm x B = ∫ I (dS x B)


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