Question

Suppose you do a calculation for the magnetic field for some situation and you find B=PR 23 for some positive constants B. and R. a) sketch this field in the yz plane, Can this field be physical ? ,/ b) If this field is physical, find the current density J associated with this magnetic field. If the magnetic field is unphysical, devise a magnetic field that is physical by adding in a term and glve an example of a functional form for that makes this new field physical. C) Using wichever B you have from part (b), find the flux A through a flat rectangular surface S of length "a in the x direction, of length in the y direction, spans 2 = -2,9 and 1 and is at fixed Z for an arbitrary 26. d) find a potential vector A that gives you the magnetic field Depo For simplicity, seek a vector potential with only an X component in rectangular coordinates. .) Calculate y Aand show it is equal to with your result from J from part (b). (U ) Calculate for the rectangular surface in part (c) and show you get the same answer as you got for part)

Answer 1

Seatter diven that a ☺ The magnetic field i B= f(y) 9 e Bo (lt az A.B=0 O dy JJ L GI+ Wollt oz)Z)-0 dz * Â = ý ý - Î Û ?? my = *.Z = . Z zo at hy Fly + 4 / [(1 + 4 z)] =0

ď fcy) -- Boa 9 integrating both Sider f(y) = -8afay г(9) - - 0, у Required magnetic 6. - 24 field + 3. (1 + 4 ZJ