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7 a using the rules of vector differentiation show that...

Question: 7 a using the rules of vector differentiation show that...

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7. (a) Using the rules of vector differentiation show that 12 (b) Using the vector identity ax (bxc)- b(a c)- c(a b) and the relation for any scalar field p(r) and vector field A(r) given in part (a), calculate the magnetic field of a magnetic dipole. Express your answer in terms of the magnetic dipole moment m, the vector function (m r)r, and some scalar functions of r, where r is the position vector and r is its length. 10 (c) A remarkable corollary of Stokess theorem of vector calculus is that for any solenoidal vector field F(r) and any two surfaces Si and S2 having the same boundary, JIs F dS- Js, F dS. Using this result, calculate the surface integral F dS in which the solenoidal field F is given by and s is the outer surface of the paraboloid之= 25-4x2-4y2 above the ry-plane Hint: Think which surface with the same boundary would lead to the easiest integration

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