Examples8.4

Examples8.4 - 1 Example 1. Find a formula for the...

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: 1 Example 1. Find a formula for the divergence of a vector field F in cylindrical coordinates. Solution. We proceed along the same lines as the discussion in the text at the end of 8.4. Consider the situation of the Figure. x y z dr rd dz r The divergence is the flux per unit volume. If F = F r e r + F e + F z k , then the flux out of this cube is, approximately (using the linear approximation), Flux [( r + dr ) F r ( r + dr,,z )- rF r ( r,,z )] d dz + [ F ( r, + d,z )- F ( r,,z )] dr dz + [ F z ( r,,z + dz )- F z ( r,,z )] dr rd ( rF r ) r dr d dz + F dr d dz + F z z rdr d dz. Thus, the flux per unit volume is div F = 1 r r ( rF r ) + 1 r F + F z z . Example 2. (a) Use Gauss theorem to show that ZZ S 1 ( F ) n dS = ZZ S 2 ( F ) n dS, where S 1 and S 2 are two surfaces having a common boundary....
View Full Document

Page1 / 2

Examples8.4 - 1 Example 1. Find a formula for the...

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