Closed integral in electromagnetics

  • Thread starter tidesong
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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 4πr2


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


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

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