Recent content by astrocytosis

Thank you, I think I understand now; my mistake was I mixed up the r in Biot-Savart with the s in cylindrical coordinates for a complete solution using Ampere’s law it must be assumed that B is zero outside (no fringing fields)

Would this be a valid solution using Ampere’s law? Seems much simpler to do it this way... also, I miscalculated the direction of the surface current before; I now see how it can contribute to the B field inside the cylinder

I am struggling to get my work to match the posted solutions to this problem. I understand part (a) but can’t get the integral to work out for (b). I know I have to use Biot-Savart and add up the components from the the surface and volume currents. The cylinder is very long, so I need to make a...

OK, I think all I need for (2) is the product rule since f*g is going to zero, but I'm still not sure how this relates to (3)

Homework Statement 1) Calculate the density of states for a free particle in a three dimensional box of linear size L. 2) Show that ##\int f \nabla g \, d^3 x=-\int g \nabla f \, d^3 x## provided that ##lim_{r \rightarrow \inf} [f(x)g(x)]=0## 3) Calculate the integral ##\int...

Homework Statement Homework Equations VD= -1/(8m2c2) [pi,[pi,Vc(r)]] VC(r) = -Ze2/r Energy shift Δ = <nlm|VD|nlm> The Attempt at a Solution I can't figure out how to evaluate the expectation values that result from the Δ equation. When I do out the commutator, I get p2V-2pVp+Vp2. This...

I thought an analytic function of an operator returned a function of its eigenvalue so it wouldn't matter... but then how can I write it in terms of T(S)?

Homework Statement Consider two operators A and B, such that [A,[A, B]] = 0 and [B,[A, B]] = 0 . Show that Exp(A+B) = Exp(A)Exp(B)Exp(-1/2 [A,B]) Hint: define Exp(As)Exp(Bs) as T(s), where s is a real parameter, differentiate T(s) with respect to s, and express the result in terms of T(s)...

Faraday's law states that EMF is the negative of the time derivative of the magnetic flux. I can find the flux for the case where there is current flowing through the wire: $$\Phi = \frac{ \mu_{0} I}{2\pi} \int_{s}^{s+a} \frac{a dr}{r} = \frac{ \mu_{0} I}{2\pi} a ln(\frac{s+a}{s})$$ But it's...

Homework Statement A square loop, side a, resistance R, lies a distance s from an infinite straight wire that carries current I (pointing to the right). Now someone cuts the wire, so I drops to zero. In what direction does the induced current in the square loop flow, and what total charge...

I lost a negative sign in the determinant. That will teach me not to skip steps :P Also, it's just ##\sqrt{2} \epsilon##

Homework Statement The Hamiltonian of a certain two-level system is: $$\hat H = \epsilon (|1 \rangle \langle 1 | - |2 \rangle \langle 2 | + |1 \rangle \langle 2 | + |2 \rangle \langle 1 |)$$ Where ##|1 \rangle, |2 \rangle## is an orthonormal basis and ##\epsilon## is a number with units of...

$$\vec J = [0 - \frac {\partial } {\partial s} (ks) ] \hat \phi = -k \hat \phi$$ so the terms cancel after all. Thanks!

Since the field outside of a solenoid is zero, only the shells with radius greater than s contribute. So the limits of integration are actually from s to R. And since K is on the surface, s=R and $$B_{K}=\mu_{0)kR$$. This almost gets me to the correct answer except I end up with $$\mu_{0)kR +...

This is my new integral with In = Jds $$ \mu_{0} \int_0^s J ds $$ $$= \mu_{0} \int_0^s k ds$$ $$ = \mu_{0} ks$$ and the contribution due to K with nI = K is $$ B = \mu_{0} nI =\mu_{0} K = \mu_{0} ks $$