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HW-2 - HW-2 1(a Let F1 x 2 z and F2 xx yy zz Calculate the...

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HW-2 1. (a) Let z x F 2 1 and z z y y x x F 2 . Calculate the divergence of and curl of 1 F and 2 F Which one can be written as the gradient of a scalar? Find a scalar that does the job. Which one can be written as a curl of a vector? Find a suitable vector potential. (b) Show that z xy y zx x yz F 3 can be written both as the gradient of a scalar and as the curl of a vector. Find scalar and vector potentials for this function. 2. Computer the divergence of the function e r e r e r v r ) cos sin ( ) sin ( ) cos ( . Check the divergence theorem of c by a direct calculation of the integrals over a hemisphere of radius R above the xy plane. 3. Check the divergence theorem for the function
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