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Unformatted text preview: HW-2 1. (a) Let F1 x 2 z and F2 xx yy zz . Calculate the divergence of and curl of F1 and F2 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 F3 yzx zxy xyz 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 v (r cos )er (r sin )e (r sin cos )e .
Check the divergence theorem of
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 v r 2 sin er 4r 2 cos e r 2 tan e .
Using the volume of the “ice-cream cone” shown below (the top surface is spherical, with
radius R and centered at the origin). 4. Check Stokes’ theorem of ( v ) dS v dl using the function v ayx bxy (a and b are constatnts) and the circular path of radius R, centered at the origin in the xy
plane. 5. Check Stokes’ theorem of ( v ) dS v dl for the function v yz , using the triangle surface shown in the following. ...
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This note was uploaded on 02/06/2010 for the course PHYSICS 11 taught by Professor Qiu during the Fall '09 term at University of California, Berkeley.
- Fall '09