Recent content by musemonkey

I figured it out but can't delete my post.

Suppose there's dielectric material in inside a parallel plate capacitor with plate charge densities ±σ. What's the electric displacement D? I've seen solutions that draw a Gaussian surface around one of the surfaces and argue that the enclosed charge is Aσ and the flux of D is Aσ therefore...

OK, that's pretty much what I expected. I'll take a photo of the screen and send it to Texas Instruments. Differentiating the antiderivative and subtracting the original integrand does give zero. The difference between what your and my calculators are producing is that mine gives a modular...

Well, first, can anyone reproduce this supposed error?

No I'm in radians. The indefinite integral result that the calculator gives is \int (~3\cos^2(t) - 1~)\sin^2(t)~dt = \frac{\sin(t)\cdot\left(6\cdot\sin^2(t)+1\right)\cdot\cos(t)}{8}-\frac{\mod(2t-\pi,2\pi)}{16} , whereas the correct answer is \int (~3\cos^2(t) - 1~)\sin^2(t)~dt =...

The integral is I = \int_0^\pi (~3\cos^2(t) - 1~)\sin^2(t)~dt . My TI-89 Titanium says I = 0 , but I know the answer (verified by hand and by mathematica) to be -\pi / 8 . I am 100% sure I entered it correctly into the calculator. What gives?

I've read that high fields arise at sharp tips of charged conductors because the surface charge density is much greater there. But since this is not a conductor but a uniformly charged surface, I'm not sure the two cases are actually related. Your point about curvature is very interesting...

Would still much appreciate any help with this question. -Musemonkey

oh I see, Euler's formula -- nice. I'll give this a try. Thanks!

Thank you Weejee. A further question: Before taking the limit, the series is -\frac{\partial V}{\partial x} = \frac{4V_0}{a}\sum_{n=0}^{\infty}e^{-(2n+1)\pi x / a} \sin(\frac{(2n+1)\pi y}{a} ) . I don't know how to get a closed form for the sum of this series, and even if I could...

1. Find the electric field at the tip of a cone of height and radius R with uniform surface charge density \sigma . I get that the field diverges at the tip, which is puzzling because it's not as though there's a point charge at the tip. I thought this sort of thing can't happen when you...

1. 1D heat conduction problem: Two rods, the first of length a , the second of length L-a with respective cross sectional areas A_1 , A_2 and heat conductivities k_1 , k_2 , are joined at one end. There are some boundary conditions on the other ends of the rods, but my question is only...

1. This is a 2D Laplace eqn problem. A semi-infinite strip of width a has a conductor held at potential V(0,a) = V_0 at one end and grounded conductors at y=0 and y=a. Find the induced surface charge \sigma (y) on the conductor at x=0. 2. Homework Equations . The potential is...

Now that you mention it, that was the plain-as-day thing to do. Thanks!

1. Two infinitely long wires running parallel to the x-axis carry uniform charge densities +\lambda and -\lambda . Find the potential at any point. Show that the equipotential surfaces are circular cylinders, and locate the axis and radius of the cylinder corresponding to a given potential...