Unformatted text preview: r 2 dc,P r2sin2#J 802 r dr r 2 ad a2* 1 a2* 2.20. Let Ei(yl, y2, y3) be the components of an unknown vector in rectan- gular Cartesian coordinates. Let each component satisfy Laplace's equation in rectangular coordinates, Show that a generalization of this equation is that Ei(x' , x 2 , x3) in curvilinear coordinates z', z2, x3 will satisfy the system of three differential equations gaPEilap = 0 I where c l a p is the second covariant derivative of Ei(x', x 2 , x3). Hint: Since g = giaGia (i not summed), G"3 is the cofactor of the element g,j in g = (g,j(, show that and that Hence....
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- Fall '05