Find the flux of a vector field

[falyusuf]

Homework Statement

Attached below.

Relevant Equations

Attached below.

Question:

Equation:

Attempt:

Can someone verify my answer?

 

[Orodruin]

First of all, your assertion

cannot be correct because it is equating a vector quantity with a scalar quantity (i.e., you are missing a vector in the expression). The reason to multiply by $\rho$ is also not "to get the correct units" although having the correct units is a reasonable check that you did things correctly. You could also multiply by $z$ and get the correct units but the result would be wrong. You therefore need a better motivation for multiplying by $\rho$.

In your last expression, you should not use $\times$ like this in an expression in vector analysis but reserve it for the vector cross product. Your result may also be simplified and evaluated exactly (i.e., there is no need to use an approximate result - the result is one of the proposed answers).