Recent content by JaneHall89

Homework Statement [/B] Consider an isotropic, homogenous dielectric sphere of radius R and constant relative permittivity ε, also permeated by a uniform free charge density ρ. Give an expression for the electrostatic potential V at the centre of the sphere by line integration of the electric...

I am not clear what you mean here. Would you be able to explain this differently please?

Im studying Maxwell's equations in a part time degree and I starting thinking in job about a particular task we perform... The situation In work we have a power cable and attach two items to it. One current-clamp-loop-generator (ferrite core wound N turns with wire) and one...

Hi, quick question with A being the lowering operator and A† the raising operator for a QHO (A A† - 1 + 1/2) ħω [Aψ] = A (A† A - 1 + 1/2) ħω ψ By taking out a factor of A. Why has the ordering of A A† swapped around? I would have thought taking out a factor of A would leave it as A (A† - 1 +...

I have done the subs after a very long day of staring at this and I think its correct but its incredibly messing and hard to simplify. For the first integral... = ((a0b) /2) x (1-e-2b/a0) Second = (a02 / 4) x ( 1 - e - 2b/a0 - 2b/a0 e-2b/a0) So I'll add them to complete. I have Just to double...

\int_{0}^{b}(e^{\dfrac{-2r}{a_{0}}}) (b-r) dr = \int_{0}^{b}-r(e^{\dfrac{-2r}{a_{0}}})+b(e^{\dfrac{-2r}{a_{0}}}) This is hurting me, I can't see how these work with standard integrals?? Everything I am trying on my paper is not working :/ Have I gone wrong somewhere else and that's why I...

hmm I'm still not seeing how to make use of the standard integrals given

E_{1}^{(1)}=\dfrac{1}{\pi a_{0}^{3}}\dfrac{q^{2}}{4\pi\varepsilon_{0}} \int_{0}^{2pi} \int_{0}^{pi}\int_{0}^{b}(e^{\dfrac{-2r}{a_{0}}}) (\dfrac{b}{r^{2}}-\dfrac{1}{r}) r2sin θ dr dθ dΦ = E_{1}^{(1)}=\dfrac{1}{\pi a_{0}^{3}}\dfrac{q^{2}}{4\pi\varepsilon_{0}} \int_{0}^{2pi}...

E_{1}^{(1)}=\dfrac{1}{\pi a_{0}^{3}}\dfrac{q^{2}}{4\pi\varepsilon_{0}} \int_{0}^{2pi} \int_{0}^{pi}\int_{0}^{b}(e^{\dfrac{-2r}{a_{0}}}) (\dfrac{b}{r^{2}}-\dfrac{1}{r}) dr dθ dΦ

But the perturbation hamilton that I have is independent of Φ,θ

I added dr

r is radius not a vector in this question. So integration is only on radius. I added dr

Homework Statement Assume that there is a deviation from Coulomb’s law at very small distances, the Coulomb potential energy between an electron and proton is given by V_{mod}(r)=\begin{cases} -\frac{q^{2}}{4\pi\varepsilon_{0}}\frac{b}{r^{2}} & 0<r\leq b\\...

So its still electrons that are being used to move around an RF/Micro circuit?

I understand in an electric circuit electrons in metallic materials move around by being directed by potential differences (fields!) I guess in a microwave circuit photons propagate as waves and are directed around and manipulated throughout the circuit by its geometry? Or have I got this...