Question

due 8am, Friday, Nov. 9nd, 2018 I. (15 pts) A loop of radius a carries a current 1 in the αφ direction. A second, small loop of radius b is placed a distance r from the origin with its center in the y-z plane and oriented so that its normal vector is an-ap, as shown below. Calculate the total flux through the small loop produced by the current in the large loop if rab. àn

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Answer 1

A loop of radius a carries a current I in the a_phi direction a second small loop of radius b is placed a distance r from the origin with its center in the y z plane and oriented so that its normal vector is a^n = -a_0 we know that phi = integral_s B d s B = mu H H rightarrow magnetic field intensity to circular current carrying loop is given by H = sigma p^2/2(e^2 + b^2)^3/2 az where p = a H = IA^2/2(a^2 + b^2)^3/2 ax now B bar = mu Ia^2/2(a^2 + b^2)^3/2 az now phi = integral_s B_z ds_z phi = integral BZ pdpd phi phi = b integral_0 2pi integral_0 Mu ia^2/2(a^2 + b^2) pdpd phi phi = mu ia^2/(a^2 + b^2) (AI) (b^2/2) \r\n phi = mu I a^2 b^2/2(a^2 + b62) loop is at point p_2 we know that dH = Iax times ar/4pi a r ar^= pap/p = ap