Recent content by dsta

Homework Statement Use a Gaussian surface and an Amperian loop to derive the electrostatic boundary conditions for the polarisation field P at an interface between electric media 1 and 2 of relative permittivities e1 and e2. (Hint: determine results for D and E first) Homework Equations...

Inside the sphere: \nabla^2V = \frac{1}{r}\frac{d}{dr}(r^2\frac{dV}{dr}) = \frac{\rho_{o}}{\epsilon_{o}} \Rightarrow V = - \frac{\rho_{o} r^2}{6\epsilon_{o}} Outside the sphere: \nabla^2V = \frac{1}{r}\frac{d}{dr}(r^2\frac{dV}{dr}) = 0 \Rightarrow r^2\frac{dV}{dr} = constant = a \Rightarrow V...

Oops sorry, I meant to say that. Okay so using the simplified form of the equation for \nabla^2V in spherical coordinates, and Poisson's equation, I was able to get the equation for V inside the sphere. For outside the sphere, the charge density is 0 obviously, so you have to use Laplace's...

Hmm okay. I'm not sure what symmetries you would need to consider to simplify \nabla^2V in spherical coordinates. Because the charge density is constant, V does not depend on r inside the sphere...I'm not sure about anything else.

Homework Statement Use Poisson's equation and Laplace's equation to determine the scalar potential inside and outside a sphere of constant charge density po. Use Coulomb's law to give the limit at very large r, and an argument from symmetry to give the value of E at r=0. Homework...

Ahh okay, that makes a lot more sense now, thanks a lot Mark. When I finish writing it up I will post my final explanation.

By /x-5/, I mean the absolute value of (x-5). I chose 1 because don't you have to break up the original improper integral into appropriate intervals to see what's going on? There are unusual things happening at x=0 and x=5, and 1 was chosen to 'link up' these separate intervals (for want of a...

Establish convergence/divergence of the following improper integral: integral from 0 to infinity of 1 / ( x^(1/3)*(/x-5/^(1/3))*(1 + sqrt(x))^0.7) ) My attempt at a solution was to break it up into 3 intergrals: 0 to 1, 1 to 5, and 5 to infinity...I showed that the first two of these...