Question

4. Magnetic dipole radiation- two loops Consider a circular current loop in the ry plane of radius b as in Section 11.1.3. Suppose there is another parallel identical loop placed a distance d above the first loop. The directions of the currents in the two loops are both counterclockwise. The long wavelength approximation is applicable. (a) Compute the total vector potential A at positions in the radiation zone. (b) Compute the total magnetic field in the radiation zone. (c) Compute the angular distribution of radiated power, and discuss the dependence on the value of d. FIGURE 11.8

4. Magnetic dipole radiation- two loops

Consider a circular current loop in the xy plane of radius b as in Section 11.1.3(See image above). Suppose there is another parallel identical loop placed a distance d above the first loop. The directions of the currents in the two loops are both counterclockwise. The long wavelength approximation is applicable.

(a) Compute the total vector potential A at positions in the radiation zone.

(b) Compute the total magnetic field in the radiation zone.

(c) Compute the angular distribution of radiated power, and discuss the dependence on the value of d.

Answer 1

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altomating 471 و اولهما = ا دة 12T Candido' -) 15. o Suppose now that we have a wire loop of radils (6) as shown in fig. and and which corrent I (t)= Ioreslwt) :: Oscillary magnent dlpole m(t)=97 b?I(+2 amo raslot) where mo = 18 Io (mariman value of dipole momput) (9) Here, scalar potensial is zero, due to unchanged loop, the restored vector potonotial is Ārst) = 40 s Tocas[wct-ovci) del x component from symmetrically placed points on either side of 2 an's will cancel. this caol wlt-olc)] 4T by @sine law 94b2-291 biasa J072452 - 2016 $mo cook! 57 = rom oi toroso for Porfect dipole, we will consider some Appottimation ch bear -9 ons on ('- mo cosmos) 4 cos [w(e-sub]E cos[w(t-sleutels xsiño cardi $ - Gr[wit-o/]] sin in because then cas (w (t-1)]= 1000 (1-865) with an orosd on [a(t-1)]. Usl Eq" (1) & (2) in equation (*) we will get coo [wle-ok)) - Yo Am [w/t-16733 In the padlanen zone come approximation is one then fristtom of above equation is negligible Āuro, U = -4o now C Magnetic field in Radiation zeong B = F xx A = - Momo? 4 Тc. Letra Chamae) cas['wce 016736 en el co[w(t-14)]3+ $$ =<57-mowe 1327263 Ano xroad) A(0,0,4) Momo (mo 4T 4ТТ C (m) sim ſo (tovy (som ras[wleme (29 369,47= to (EXB); :É=== Hom w? .. $19,1) ile de utic .. Total Power Padtahin <97=f<szda = lo miwi 12TT 3

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