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Given a short solenoid of length L and a radius R, placed paralellel and symmetrically about the z-axis. There are N closely wound turns of wire carrying a current I. (a) Show from first principle, the B field at (x =0,y=0, and Z <l 2)="" of="" the="" solenoid="" is="" given="" by,<br="">z+L/2 (R2+(L12-2)2 z-L/2 - When setting up the problem, use the primed coordinates to represent the source position, and umprimed coordinates for the field position. (b) Show if R <<l, the="" field="" at="" ends="" is="" half="" that="" middle.="" is:<br="">(c) Show at large distances, i.e = 4 2m , where m is the dipole moment of the solenoid. Extract Z or Z +L 12 from expressions involving Z and expand binomially the rest as a power series in L / Z up to and including the 3rd order. </l,></l>

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