Homework Statement
Suppose you have a disk of radius r at x=y=z=0 with its normal pointing up along the z-axis. The disk radiates with specific intensity I(\theta) from its upper surface. Imagine the observer plane is at z=Z, where Z is much greater than r. Let I(\theta) = I = constant...
Homework Statement
It is known that there is a 36% probability of obtaining S_z = \hbar/2 and therefore a 64% chance of obtaining S_z = -\hbar/2 if a measurement of S_z is carried out on a spin 1/2 particle. In addition, it is known that the probability of finding the particle with S_x =...
Hello all,
I'm trying to compile a list of schools (mainly in the US) that offer Ph.D. programs with research in radio astronomy.
Here's what I've come up with so far:
Caltech
Cornell
Harvard
New Mexico Tech
Ohio State University
UC Berkley
UC Los Angeles
UC Santa Cruz
University of Arizona...
Homework Statement
A string of length l has a zero initial velocity and a displacement y_{0}(x) as shown. (This initial displacement might be caused by stopping the string at the center and plucking half of it). Find the displacement as a function of x and t.
See the following link for...
Homework Statement
Hi all,
Here's the problem:
Prove, in tensor notation, that the triple scalar product of (A x B), (B x C), and (C x A), is equal to the square of the triple scalar product of A, B, and C.
Homework Equations
The Attempt at a Solution
I started by looking at the triple...
Homework Statement
A puck with mass m sits on a horizontal, frictionless table attached to four identical springs (constant k and unstreched length l_0). The initial lengths of the spring a are not equal to the unstretched lengths. Find the potential for small displacements x,y and show that...
Hi all,
My classmates and I have been at this problem for some time, and it doesn't look like we're getting anywhere. We'd really love any help in the right direction!
Homework Statement
A lawn sprinkler is made from a spherical cap (max angle = 45\)
with a large number of...
Homework Statement
Find the center of mass of a solid of density \delta = 1 enclosed by the spherical coordinate surface \rho = 1-cos\phi.
Homework Equations
The Attempt at a Solution
I'm a bit confused about how to start here, mainly because the surface is defined by spherical...
Homework Statement
Set up triple integrals for the integral of f(x,y,z)=6+4y over the region in the first octant that is bounded by the cone z=(x^2+y^2), the cylinder x^2+y^2=1 and the coordinate planes in rectangular, cylindrical, and spherical coordinates.
Homework Equations...
Homework Statement
Find the volume enclosed by the spherical coordinate surface ρ = 2sin∅
Homework Equations
dV = ∫∫∫(ρ^2)sin∅dρd∅dθ
The Attempt at a Solution
(Sorry about my notation!)
Alright, here's what I've done so far...
Since the region is a torus, centered...
Homework Statement
Find the volume of the region bounded by the cylinder x^2 + y^2 =4 and the planes z=0, and x+z=3.
Homework Equations
V = ∫∫∫dzdxdy
V=∫∫∫rdrdθ
The Attempt at a Solution
Alright, so I feel as though I'm missing a step somewhere along the way, but here's what I've gotten...
Proof -- Express in Clyndrical Coordinates
Homework Statement
Show that when you express ds^2 = dx^2 + dy^2 +dz^2 in cylindrical coordinates, you get ds^2 = dr^2 + r^2d^2 + dz^2.
Homework Equations
x=rcosθ
y=rsinθ
z=z
The Attempt at a Solution
EDIT// I was really over thinking...
Homework Statement
Find a parametrization of the equation of the line formed by the points A, B, and P.
A(2,-1,3) B(4,3,1) P(3,1,2)
Homework Equations
x=x_0+v_1*t
y=y_0+v_2*t
z=z_0+v_3*t
The Attempt at a Solution
Alright, so, I've already determined that P is equidistant from the points...
Homework Statement
The graph in the figure shows the electric field strength (not the field lines) as a function of distance from the center for a pair of concentric uniformly charged spheres. Which of the following situations could the graph plausibly represent? (There may be more than one...
Homework Statement
Ʃ(1 to infinity) (2/3)^(3n)
Homework Equations
For a geometric series, the series converges to a/1-r
The Attempt at a Solution
I'm really just confused about how to manipulate this so that it has a form of ar^n, especially since it starts at 1 rather than 0. I know that...
Homework Statement
I'm just trying to understand a few things about the Maclaurin series for e^x...
So, in one case, if you have a series from 1 to infinity of [(-1)^n * 3^n ]/n!, how is it that it is equal to e^-3 - 1? I understand the e^-3 part, as -3 is simply our x value from the...
Homework Statement
I'm given this series and asked whether it converges, absolutely converges, or diverges.
Ʃ(n=0 to infinity) [2(-1^n)(3^(n+1))]/5^n
Homework Equations
The Attempt at a Solution
The answer states that it is absolutely convergent, and that it converges to 15/4. Everything...
Homework Statement
An inductor has a current I(t) = (0.480 A) cos[(280 s-1)t] flowing through it. If the maximum emf across the inductor is equal to 0.490 V, what is the self-inductance of the inductor?
Homework Equations
ε = -L*di/dt
The Attempt at a Solution
I would have that...
Homework Statement
A charged capacitor is connected to an ideal inductor to form an LC circuit with a frequency of oscillation f = 1.6 Hz. At time t = 0 the capacitor is fully charged. At a given instant later the charge on the capacitor is measured to be 3.0 μC and the current in the circuit...
Homework Statement
Expand f(x) = x/(x+1) in a taylor series about a=10.
Homework Equations
f(x) = Ʃ (f^n(a)*(x-a)^n / n!
The Attempt at a Solution
I'm having a hard time arriving at the correct answer..I think I'm definitely getting lost somewhere along the way. Here's what I've...
Homework Statement
The figure shows an end view of two long, parallel wires perpendicular to the xy-plane, each carrying a current I but in opposite directions.
Derive the expression for the magnitude of B at any point on the x-axis in terms of the x-coordinate.
Homework Equations...
Homework Statement
Just trying to understand some concepts regarding this particular circuit configuration.
When the switch is open, I understand the bulbs B and C form a loop, and therefore the potential difference across each is the same. I don't understand why -- when the switch is...
Homework Statement
I don't have any particular problems I need help with. I'm just trying to wrap my head around some of the equations and their meanings. Any clarification would be great!
We have from Kepler's 3rd Law the following:
The period squared is proportional to the semi-major...
NASA's Stardust Mission -- Interplanetary Dust Particles
Hello all,
I'm currently working on a research paper about IDPs, and I'd like to spend some time discussing NASA's Stardust Mission.
I'm wondering if anyone might know of some links to some scholarly articles concerning the matter...
Homework Statement
A huge (essentially infinite) horizontal nonconducting sheet 10.0 cm thick has charge uniformly spread over both faces. The upper face carries +95.0 nC/m2 while the lower face carries -25.0 nC/ m2. What is the magnitude of the electric field at a point within the sheet...
Homework Statement
A cone is resting on a tabletop as shown in the figure with its face horizontal. A uniform electric field of magnitude 4550 N/C points vertically upward. How much electric flux passes through the sloping side surface area of the cone?
Homework Equations
flux = ∫...
EDIT: That ought to be, "Dielectrics," of course :)
Homework Statement
An air capacitor is made by using two flat plates, each with area A, separated by a distance d. Then a metal slab having thickness a (less than d) and the same shape and size as the plates is inserted between them...
Homework Statement
The capacitors in the figure are initially uncharged and are connected, as in the diagram, with switch S open. The applied potential difference is V_ab = 210V.
a) What is the potential difference V_cd?
b) What is the potential difference across each capacitor...
Homework Statement
Consider a capacitor that consists of two metal plates of nonzero thickness separated by a positive distance d. When such a capacitor is connected across the terminals of a battery with emf EMF, two things happen simultaneously: Charge flows from one plate to another, and a...
Homework Statement
A hollow cylinder of radius r and height h has a total charge q uniformly distributed over its surface. The axis of the cylinder coincides with the z axis, and the cylinder is centered at the origin, as shown in the figure.
What is the electric potential V at the...