Hello all!
Homework Statement
Consider a cylindrical cavity with length "d" and radius "a". Find the corresponding electric field, and the dispersion relation therein.
Homework Equations
Maxwell's equations.
The Attempt at a Solution
I tried to solve the appropriate vector Helmholtz...
TSny,
Thank you very much! I finally have my head around the solution. You're absolutely right(as I see it, now) that the view of fields nearest to the conductor can be considered through their analogues within the slab. And furthermore, the normal components are related through the need to...
Thank you both!
Thanks so much for your efforts, BvU & TSny! Sorry it has taken me a while to reply!
I looked over your suggestions, BvU, and I fear that such an integral equation would be impossible to solve, without a priori working out σ -- i.e. the surface charge distribution. Furthermore...
Thank you for replying.
It was in fact my idea to develop a series formulation of the potential \frac{1}{|\vec{r}-\vec{r}'|} with Legendre's polynomials, as that would give me an orthonormal basis, which in turn should have made finding the coefficients easier. Plus, it seemed like the natural...
At θ=0 the vector would be along the z-axis, aligned with the external point-charge. V is not zero there.
If I plug in θ=Pi/2, I would indeed see that theta is perpendicular to the surface. Still, since I don't know the induced surface charge dist., I doesn't advance me anywhere.
I don't quite follow
Sorry,
I don't quite get that.
The plane (x-y) which is located where z=0 is attained when θ = π/2, since, in the the (standard) spherical system: r_z = r \cos(\theta).
If I were to apply θ=0 on E, I would obtain the field perpendicular to the surface, which, according...
Thanks for your response..
Thanks for your reply.
Unfortunately, taking the gradient of E, and projecting onto the radial direction, at θ=Pi/2 creates a problem.
It does, as you rightly point out, equal Etangential, and that in turn should be zero; however, when taking it, I obtain again(for...
Hello everyone!
Homework Statement
A charge, +q, is placed above an infinite conducting slab located at z<=0, at (0,0,d). Find the potential everywhere in space, without using the image-charge method.
Homework Equations
Laplace's equation(and its solution in spherical coordinates).
(CGS units...
Now, it's finally clear!
Stephen,
Thanks again for your patient and diligent aid here! it's finally dawned on me(and I'm sorry it has taken so long).
I now see that I should have accounted for the various values Y≤t could take, irrespective of X; and obviously, as you point out, the...
You are, of course, correct!
You're obviously right. I can't believe I didn't detect such a boneheaded mistake, sooner; thank you!
I see I should have written that equality, using the LTP, in this manner:
P(Y \leq t) = \sum_i P(Y \leq t \cap A_i)
Where again A_i form the domains of Y...