2. In the videos, we found the Neumann integral for the mutual inductance M21 between two concentric circles of radii A and a, respectively, at a distance from each other (Maxwell's inductance), 26 27 M21 HO 47 Aa cos( 92 - 91d9d-02 V 42 +42 +52 - 2.Aa cos(92 - 91) 2.1. Find a similar Neumann integral (no need to solve it) for the case of two concentric ellipses with semi-major axis A and a and semi-minor axis B and b, respectively. Assume the two ellipses belong to two parallel planes at a distance from each other, as shown in Fig. 2.2. [10 points) 2.2. Show that the result found in 2.1 reduces to the Neumann integral for two concentric circles when A = B and a = b. Consider then the elliptic integrals solution M21 -MOV Aa av AD[(1 3)"Q+; cu) Assume A = 0 = 1 m and 8 = -1/4, with r = 1 mm. Under these conditions, 8 can be assumed to be small. Using these numerical values and following closely all derivations in the videos on the Maxwell's inductance, compare the approximate result for M2 when considering the first two terms (i.e., up to k) in the series expansions for F(k) and (k) (F) [+()*+*+(4:45)*+..] EVE) - (--) --0353 to the approximate result obtained when considering just the first term (i.e., In 4/ k, and 1, respectively) in the series expansions 4 4 FIn ku ki 1 E~1+ki In 2. In the videos, we found the Neumann integral for the mutual inductance M21 between two concentric circles of radii A and a, respectively, at a distance from each other (Maxwell's inductance), 26 27 M21 HO 47 Aa cos( 92 - 91d9d-02 V 42 +42 +52 - 2.Aa cos(92 - 91) 2.1. Find a similar Neumann integral (no need to solve it) for the case of two concentric ellipses with semi-major axis A and a and semi-minor axis B and b, respectively. Assume the two ellipses belong to two parallel planes at a distance from each other, as shown in Fig. 2.2. [10 points) 2.2. Show that the result found in 2.1 reduces to the Neumann integral for two concentric circles when A = B and a = b. Consider then the elliptic integrals solution M21 -MOV Aa av AD[(1 3)"Q+; cu) Assume A = 0 = 1 m and 8 = -1/4, with r = 1 mm. Under these conditions, 8 can be assumed to be small. Using these numerical values and following closely all derivations in the videos on the Maxwell's inductance, compare the approximate result for M2 when considering the first two terms (i.e., up to k) in the series expansions for F(k) and (k) (F) [+()*+*+(4:45)*+..] EVE) - (--) --0353 to the approximate result obtained when considering just the first term (i.e., In 4/ k, and 1, respectively) in the series expansions 4 4 FIn ku ki 1 E~1+ki In
