We have to "closely spaced" frequencies f1 and f2. "The moving mirror moves at a constant speed v. Explain how the Doppler effect on the light reflected from the moving mirror affects the recorded signal as a function of time. Estimate the value of v required to resolve the freq. difference of...
We are asked to explain what is meant by a "well behaved function" which represents a physical phenomenon. I know that it has to be continuous, and differentiable at all points (therefore we need the gradient to be continuous), but I'm not sure if derivatives of all orders need to be continuous...
We have the eigenvalue equation
R(x)*(Wn*2)*Yn(x) = -T (d^2)[Yn(x)]/dx
T the tension is a constant
R(x) is the weight function, Wn is the eigenvalue of the nth normal mode and Yn is the nth normal mode eigenfunction. We have to show that the integral of (Yn(x)*Ym(x)*R(x)) between the...
we have a non magnetic but anisotropic dielectric medium which has the following relationships between D and E
Dx = k1*Ex, Dy = k2*Ey, Dz = k3*Ez
we have to show that waves propogate in the z-dir'n at one speed only.
I can't get the wave eq'n to fall out. Usually you just use...
surely energy flows from the circuit to which the capacitor is connected and not from the surroundings?
Also if we consider energy being dissipated in a wire we get a similar situation. let the current flow be into the page. this is also the direction of the electric field. by the right hand...
In a parallel plate capacitor with circular plates we're asked to find the magnitude and direction of the poynting vector, which logically should be pointing radially outwards. Let us say that the top plate is positively charged and the bottom is negatively charged. Therefore we have an E-field...
We have to integrate [(lnx)^2)/(1+(x^2)) from zero to infinity.
I have set up the correct complex integral with a branch cut along the negative y-axis, but I end up with an integral of [(lnx)^2](1+x^2) from minus infinity to zero. I'm not sure how to deal with this.
In complex analysis we say that for fn's like lnz we apply a branch cut along positive x-axis to make sure it's single valued. i.e restrict theta s.t 0<=theta<2Pi but we never allow theta to equal 2Pi as this would make lnz take on 2nd value.
Let us integrate around a contour which goes from...
"by what factor may the glare off water be reduced when the sun is at
a) 45 degrees above the horizon
b)60 degrees above the horizon
n.b refractive index of water is 1.33"
I have derived the fresnel reflection coefficients for the cases when E is perpendicular to the plane of...
We have a question that asks us what thickness of copper is necessary to achieve optical reflectivity. I know that the answer is just basically several times the skin depth (says 10 times). the only problem is that this contradicts a previous result that I've seen. We can prove that when a wave...
In Boas on p.595 there's an FCV proof for finding the order of a pole.
It says to write f(z) as g(z)/[(z-zo)^n] and then write g(z) as a0 + a1(z-z0) ... etc. and that we can deduce that the Laurent series for f(z) begins with (z-z0)^(-n) unless a0 = 0 i.e g(z0) = 0. Therefore the order of the...
I'm having trouble determining the order of the pole of
[exp(iz) - 1]/((z^2) + 4) at z=2i
I know I can't just expand the exponential as 1 + iz + [(iz)^2]/2 ...
because this formula only works near the origin. Can I still use Taylor's theorem to find the expansion at z=2i (i.e does...
this question supposes the existence of magnetic monopoles, and then redefines maxwell's eqn's as follows
div(B) = dm
curl(E) = -dB/dt - Jm
where Jm is the magnetic current density, and dm is the magnetix charge density
we are asked to find the energy acquired by a monopole with Dirac...
We have to find the capacitance and inductance of a pair of cylindrical conductors of radius r and at a distance d b away from each other. I get the following expressions
C = 2Pi*epsilon0/ln(b/a)
L = Mu0/2Pi *ln(b/a)
We now have a cylindrical conductor a distance d above an infinite...
I'm confused about the status of Vm. We are asked under what circumstances we can write B = - Mu0*grad(Vm).
I think the idea is that when there is no current density (displacement or conduction) we can write curl(B) = 0. Therefore we can write B as a grad of a scalar potential, as curl grad = 0...