flux integrals over spheres and cylinders

peacefreak77

New member
Joined
Aug 22, 2006
Messages
32
My math book tells me the equation for a flux integral over a sphere for instance is the integral(over the region) of the force vector field in terms of rho, theta, and phi, dotted with sin(phi)*cos(theta)ihat+sin(phi)*sin(theta)jhat+cos(phi)khat, multiplied by R^2*sin(phi), dzdtheta, where R is the radius, or phi.

That is all great when the force vector field given is in terms of ihat, jhat, and khat. However, my homework has force vector fields in terms of rhat, thetahat, and zhat, or for spherical roehat, thetahat, phihat.

So I don't know how to either change my force vector field from r,theta,z to x,y,z (in polar terms) or to change what I'm supposed to dot it with to r,theta,z coordinates.

One of the problems: Calculate the flux of the vector field F=(4rho^2)thetahat through the surface of the sphere centered on the origin with radius 4

How to I change 4rho^2thetahat to an i, j, k vector that I can dot with cos(theta)ihat+sin(theta)jhat, or change cos(theta)ihat+sin(theta)jhat to a rho, theta, phi vector that I can dot with 4rho^2thetahat?

Sorry that was so long. I am desperate for help, though, and any is very much appreciated.
 
Top