Use Stokes Theorem and Maxwells law to derive equation
- Thread starter sdsu619
- Start date
Not seeing any work, I assume you heed help setting it up.
The first thing to do is to write down Stokes' Theorem. Quoting from Wikipedia,
Slightly different notation, but how does that relate to the problem at hand? It looks like you can prove eq.(1) in about two steps - except for the minus sign - I haven't looked closely enough to see why the right side of eq.(1) is negative. Must have to do with defining the sense of surface S, whether B points out or in. Right-hand rule?
The work done on a charge Q is Q*integral(E·ds) around the closed curve, which (by eq.(1)) is equal to the surface integral of normal component of dB/dt.
If you need more help, show us your work, so we can tell where you are getting stuck.
So I figured out the derivation part of the problem, but am having trouble with the actual question.
The question was revised so that
So that means the curl(E) now equals <3y, -xz, 0>
The part Im having trouble with is parametrizing the surface. I attempted to set 2z = r since 2z = x^2 + y^2
Then plug in 1-y for z resulting in
r = 2 - 2y?
Not sure if this was the right thing to do, as i dont know where to go after that
The question was revised so that
So that means the curl(E) now equals <3y, -xz, 0>
The part Im having trouble with is parametrizing the surface. I attempted to set 2z = r since 2z = x^2 + y^2
Then plug in 1-y for z resulting in
r = 2 - 2y?
Not sure if this was the right thing to do, as i dont know where to go after that
That may prove useful when finding limits of integration.
Surface S: x^2 + y^2 - 2z = 0, unit normal S = (x, y, -1)/sqrt(x^2+y^2+1) = (x, y, -1)/sqrt(2z + 1)
dB/dt · S = (3xy - xyz + 0)/sqrt(2z + 1) = xy(3 - z)/sqrt(2z + 1)
Can you make anything of that?