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www.GOALias.blogspot.comMoving Charges andMagnetism2µ0RB =32xNote that the area of the loop A = πR 2 . Thus,µ0IAB =32 π xAs earlier, we define the magnetic moment m to have a magnitude IA,m = I A. Hence,µ0mB ;32 ð xµ0 2m=3[4.31(a)]4ðxThe expression of Eq. [4.31(a)] is very similar to an expression obtainedearlier for the electric field of a dipole. The similarity may be seen if wesubstitute,µ → 1/ ε0 0m → pe(electrostatic dipole)B → E (electrostatic field)We then obtain,2peE =34 π ε0xwhich is precisely the field for an electric dipole at a point on its axis.considered in Chapter 1, Section 1.10 [Eq. (1.20)].It can be shown that the above analogy can be carried further. Wehad found in Chapter 1 that the electric field on the perpendicular bisectorof the dipole is given by [See Eq.(1.21)],peE ;34πεx0where x is the distance from the dipole. If we replace p à m and µ0→ 1/ ε0in the above expression, we obtain the result for B for a point in theplane of the loop at a distance x from the centre. For x >>R,µ0 mB ; ; x >> R3 [4.31(b)]4πxThe results given by Eqs. [4.31(a)] and [4.31(b)] become exact for apoint magnetic dipole.The results obtained above can be shown to apply to any planar loop:a planar current loop is equivalent to a magnetic dipole of dipole momentm = I A, which is the analogue of electric dipole moment p. Note, however,a fundamental difference: an electric dipole is built up of two elementaryunits — the charges (or electric monopoles). In magnetism, a magneticdipole (or a current loop) is the most elementary element. The equivalentof electric charges, i.e., magnetic monopoles, are not known to exist.We have shown that a current loop (i) produces a magnetic field (seeFig. 4.12) and behaves like a magnetic dipole at large distances, and161