Homework Statement
A system in a state \frac{1}{\sqrt{2}}(\left<\phi\right| + \left<\psi\right|) undergoes an interaction with a second system (which is initially in \left<\alpha\right|) and ands up in an entangled state \frac{1}{\sqrt{2}}\left(\left\langle\phi\right| \otimes...
Does anybody have any tips for doing this well? Frankly, I'm pretty terrible at it. I mean, once I get a small amount going through, I can do a little bit of optimisation by adjusting the angle of the fibre in one direction, and then adjusting the angle of the incident beam along the same plane...
Homework Statement
I'm doing Millikan's oil drop experiment in a lab. I've got a set of measurements and all that, but in analysis of the data I can't seem to get values for the charges on individual drops that seem reasonable. I find that each drop is carrying between 10 and 300 elementary...
Okay, I need boundary conditions to find the solutions, right? I know that A is continuous everywhere. (Incidentally, I realized that I forgot to write \nabla^2{\bf{A}}_x = 0 outside the sheet). A is 0 at y = \infty. So that gives me
\frac{\partial^2 A^{in}_x}{\partial x^2} + \frac{\partial^2...
Homework Statement
An infinite sheet of copper conductor, thickness t, lies in the xz-plane. The sides of the sheet intersect the y-axis at y=\pm\frac{t}{2}. The current density in the sheet is given by:
{\bf{j}}({\bf{r}}) = \begin{cases}
j_0\left(\frac{y}{t}\right)^2{\bf{\hat{x}}}, &...
Homework Statement
An alternating current I = I_0 \cos(\omega t) flows down a long straight wire and returns along a coaxial tube of radius a.
By constructing an appropriate Amperian loop or otherwise, and assuming that the induced electric field E goes to zero as the distance from the...
Homework Statement
A particle is moving freely in the x direction.
Find the initially allowed (i.e. at t=0) values of \langle x^2 \rangle and \langle p^2 \rangle, and find equations of motion for \Delta x and \Delta p,
Homework Equations
\frac{d}{dt}\langle A\rangle =...
Homework Statement
A concave astronomical telescope mirror may be made by rotating a circular tank of mercury. Find an expression for the shape of the surface in terms of the density of mercury, the radius from the centre, and the rotation rate.
Homework Equations
v = r \omega
The...
The problem says that you're moving along a straight radial line - imagine that the disk has a straight line from the circumference to the centre, and, as the disk rotates, you start at the centre and walk along this line to the edge. If you were standing in one spot on the disk, then you would...
P = \frac{1}{3}\rho {v_{rms}}^2
\rho = \frac{m}{V}
P = \frac{m}{3V} {v_{rms}}^2
v_{rms} = \sqrt{\frac{3PV}{m}}
In some amount of time dt, if A_h is the area of the hole, the amount of mass dm that passes through the hole is
dm = A_h\cdot \sqrt{\frac{3PV}{m}}dt
Rearranging:
\sqrt{\frac{m}{P}}dm =...
Homework Statement
A space capsule, which may be treated as a sphere of radius 10m, is hit by a micrometeorite which makes a hole of diameter 2mm in its skin. Estimate how long it will take for the air pressure to drop by 30%. Avogadro's number is about 6 \times 10^{23}
Homework Equations...