finalreview - 1. (20 points) Find the total flux upward...

Info iconThis preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: 1. (20 points) Find the total flux upward throught the upper hemisphere ( z 0) of the sphere x 2 + y 2 + z 2 = a 2 of the vector field T ( x, y, z ) = x 3 3 i + yz 2 + e zx j + ( zy 2 + y + 2 + sin( x 3 )) k . Hint Use the divergence theorem around some simple region. youll also need to compute one more flux integral. Use symmetry. 2. (20 points) Suppose a vector field is defined by F ( x, y, z ) = ( y 2 z ) i +(2 xyz ) j + ( xy 2 + 4 z ) k . a) Determine whether there is a scalar function ( x, y, z ) defined everywhere in space such that 5 = F . If there is such a , find one; if there are none, explain why not. b) Determine whether there is a vector field A ( x, y, z ) defined everywhere in space such that 5 A = F . If there is such an A , find one; if there are none, explain why not. c) Compute the integral R W F T ds where W is the circular helix whose position vector is given by R ( t ) = (cos( t )) i +(sin( t )) j + t k for t [0 , ]. Use information]....
View Full Document

Ask a homework question - tutors are online