Maybe my question is a little confusing.
Suppose we have a long metal strip which is very thin and we apply a fixed potential on it. How to calculate the potential around the metal strip?
In order to calculate the potential, we must know the surface charge on the metal. From textbook, we...
Does anyone know how to calculate the capacitance of a metal strip of width 2a and infinitesimal thickness? The length of the metal strip is much larger than its width.
Thanks a lot!
Thanks guys.
After reading about your posts, I came up with the following understanding:
Suppose Matrix(A) transforms the geometrical shape whose edges are row vectors of identity matrix I. The edges of resulted geometrical shape are the column vectors of Matrix(A).
For the geometrical...
I have come across a theorem which says that det(A)=0 if and only if the row (or column) vectors of A are linearly dependent.
I can understand the proof for it, but fails to figure out what's the essential meaning of this theorem. Can someone provide me a simple intuitutive understanding of...
I think I understand the situation here. The complex number \beta not only includes the information about the magnitude but also the information about the phase \theta, so it is not a good way to look at the limit of
\frac{e^{\beta(\varepsilon_{F}-\varepsilon_{i})}}{\beta}
from the purely...
Thank you!
I know how to evaluate the line integral now.
\beta -\gamma=R e^{i\theta}
d\beta =d(\beta-\gamma)=i\cdot R \cdot e^{i\theta}d\theta
\int_{C^1}\frac{e^{\beta(\varepsilon_{F}-\varepsilon_i)}}{\beta}d\beta=\int_{\pi/2}^{3\pi/2}\frac{e^{(\gamma + R...
Thanks!
I should state it more clearly. Beta here is a complex number, and |beta|--> infinity. My last limit is confusing. It is the length of arc C2 at |beta|--> infinity, which is \lim_{R\rightarrow \infty}\pi R.
The integral was taken from a book, and it was said in that book that...
\frac{1}{2\pi i}\int_{\gamma-i\infty}^{\gamma+i\infty}\frac{e^{\beta(\varepsilon_{F}-\varepsilon_i)}}{\beta}d\beta=?
When \varepsilon_{F}>\varepsilon_{i} , the contour is C1 + C2 (see the attached file). Let \beta\rightarrow \infty, the integration along C2 vanishes. Then the result is given...