Closed integral in electromagnetics

  • Thread starter tidesong
  • Start date
  • #1
tidesong

Main Question or Discussion Point

Well i'm studying this under engineering but its also maths so I posted this here and hope its in the right forum

The question is: When using Gauss's Law i have this equation in my notes: total charge enclosed by surface = closed integral of ( D .ds) over S

the next line (in my notes) equates this to Dr( closed integral of dS over S)

Is this a mathematical manipulation, or is this due to some law? And is Dr just a constant or does it have some meaning? Thanks.
 

Answers and Replies

  • #2
841
1
Can you tell me what any of the symbols are supposed to mean? I could try to guess..

You have the integral,

integral D.dS

If the surface S is a sphere, the normal area vector dS is radial, so D.dS is Dr, i.e. the radial component of the D vector. So you can reduce it to,

integral Dr dS

If you also assume that the D field is spherically symmetric, then the value of D (and hence Dr) is constant over the surface of a sphere (since it is at a fixed radius); you can then pull it out of the integral,

Dr integral dS

The integral of the area element is just the area of the sphere, so you obtain

Dr 4πr2
 
  • #3
tidesong
Ah thanks! If Dr is the radial component then it makes sense! I'm trying to guess what my notes mean too :P
 
  • #4
iodoethane
Yeah! Our notes are so lousy! Thanks for helping out =)
 

Related Threads on Closed integral in electromagnetics

  • Last Post
2
Replies
31
Views
32K
Replies
1
Views
2K
Replies
8
Views
15K
Replies
9
Views
7K
Replies
0
Views
1K
Replies
5
Views
969
Replies
1
Views
808
  • Last Post
Replies
5
Views
3K
Replies
2
Views
2K
Replies
2
Views
3K
Top