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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 c 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. ...
View Full Document

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.

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online