question_answer 46)

    Verify the Ampere's law for magnetic field of a point dipole of dipole moment .  Take C as the closed curve running clockwise along (i) the z-axis from z = a > 0 to z = R ; (ii) along the quarter circle of radius R and centre at the origin, in the first quadrant of -z plane ; (iii) along the -axis from  = R to  = , and (iv) along the quarter circle of radius  and centre at the origin in the first quadrant of -z plane.

Answer:

                  Refer Fig. 3(EP).18, From P to Q, every point on the z-axis lies at the axial line of magnetic dipole of moment . Magnetic field            induction at a point distance z from the magnetic dipole of moment  is                 (i) Along z-axis from P to Q.                                           (ii) Along the quarter circle QS of radius R. Refer Fig. 3(EP).19, point A lies on the equatorial line of the magnetic dipole of moment M sin . Magnetic field at point A on the circular arc is                                               (iii) Along -axis over the path ST. Fig. 3(EP).20, every point lies on the equatorial line of magnetic dipole. Magnetic field            induction at a point distance from the dipole is [ angle between and  is ] (iv) Along the quarter circle TP of radius a. Refer Fig. 3(EP).21. Refer case (ii) ; Line integral of  along the quarter circle TP of radius a is