# Closed integral in electromagnetics

tidesong
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.

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 4&pi;r2

tidesong
Ah thanks! If Dr is the radial component then it makes sense! I'm trying to guess what my notes mean too :P

iodoethane
Yeah! Our notes are so lousy! Thanks for helping out =)