A small loop of wire (radius a ) is held a distance z above the center of a larg

Question

A small loop of wire (radius a) is held a distance z above the center of a large loop (radius b). the planes of the two loops are parallel, and perpindicular to the common axis.

A) If current I flows in the big loop. Find the flux through the little loop. (the liitle loop is so small that you may consider the field of the big loop to be essentialy constant)

B) If current I flows in the little loops. find the flux through the big loop. (the little loops is so small that you may treat it as a magnetic diple)

C) find the mutual inductances, and confirm that M12=M21

Explanation / Answer

A) 1 = Z B2 ·da1

  B(z) = (µoI/ 2 )R2 /(R2 +z2)3/2

  1 = B2·a2

= µoa2b2I /2(b2 + z2)3/2r

B) 2 = B1 ·da2

  Bdip = (µom /4r3 )(2cosˆr+sinˆ)

C)Bdip = (µom /4r3 )(2cosˆr+sinˆ)

  r = sin

= b b2 +z2

r= b (8) b2 +z2

=(µoIa2/2(b2+z2) )(b2/b2+z2)

=µoa2b2I/2(b2+z2)3/2

M12=1I=µoa2b22(b2+z2)3/2

,M21=2I=µoa2b22(b2+z2)3/2

M12 =M21

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