Question

Consider a two-dimensional potential problem for a region bounded by four planes x=0, y=0, and y=1....

Consider a two-dimensional potential problem for a region bounded by four planes x=0, y=0, and y=1. There are no charges inside the bounded region. The boundaries at x=0, x=1, and y=0 are held at zero potential. The potential at the boundary y=1 is given by V(x,1)=V0sin(pi*x)

a.) find the electrostatic potential V(x,y) everywhere inside this region by solving the Laplace equation in two dimensions using the method of separation of variables.

b.) Calculate the surface charge density on the boundary y=0.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Consider the set D which is the triangular region bounded by y=x, x=0, y=4 and the...
Consider the set D which is the triangular region bounded by y=x, x=0, y=4 and the boundary of this triangular region. Find the absolute maximum and minimum values of f(x,y) = x2 -xy +y2+1 on D. Make sure you show work for testing for critical values inside the region and on the lines that make up the boundary as part of your work shown
Find the center mass of the solid bounded by planes x+y+z=1, x=0 y=0, and z=0, assuming...
Find the center mass of the solid bounded by planes x+y+z=1, x=0 y=0, and z=0, assuming a mass density of ρ(x,y,z)=7sqrt(z) Xcm Ycm Z cm
Consider the function f(x,y) = tan((x−3y)/2)/(x + y) and the region bounded by y = x,...
Consider the function f(x,y) = tan((x−3y)/2)/(x + y) and the region bounded by y = x, y = x−1, y = 0 and y = −1/2. Using the change-of-variables u = x−3y and v = x + y, setup the integral of f over this region.
Consider the region bounded by y = x2, y = 1, and the y-axis, for x...
Consider the region bounded by y = x2, y = 1, and the y-axis, for x ≥ 0. Find the volume of the solid. The solid obtained by rotating the region around the y-axis.
An electrodynamics question. Due is tomorrow noon. I have no idea where to start. 1. A...
An electrodynamics question. Due is tomorrow noon. I have no idea where to start. 1. A long conducting pipe has a rectangular cross section with sides of lengths a and b. One face of the pipe is maintained at a constant potential V = V_0 while the other 3 faces are grounded (V = 0). Using separation of variables, find the potential for points inside the pipe V (x,y). I solved this question using boundary conditions, Fourier sine series, and...
Given that D is a region bounded by x = 0, y = 2x, and y...
Given that D is a region bounded by x = 0, y = 2x, and y = 2. Given: ∫ ∫ x y dA , where D is the region bounded by x = 0, y = 2x, and y = 2. D Set up iterated integrals (2 sets) for both orders of integration. Need not evaluate the Integrals. Hint: Draw a graph of the region D. Consider D as a Type 1 or Type 2 region. Extra credit problem
4. Let W be the three dimensional solid inside the sphere x^2 + y^2 + z^2...
4. Let W be the three dimensional solid inside the sphere x^2 + y^2 + z^2 = 1 and bounded by the planes x = y, z = 0 and x = 0 in the first octant. Express ∫∫∫ W z dV in spherical coordinates.
Let R be the region bounded by y = x2 + 1, y = 0, x...
Let R be the region bounded by y = x2 + 1, y = 0, x = 1, and x = 2. Graph the region R. Find the volume of the solid generated when R is revolved about the y-axis using (a) the Washer Method and (b) the Shell Method.
Consider a lamina of density ρ = 1 the region bounded by the x-axis, the y-axis,...
Consider a lamina of density ρ = 1 the region bounded by the x-axis, the y-axis, the line x = 5, and the curve y = e^x. Find the centroid ( ̄x, ̄y). (Simplify, but leave your answer as an exact expression not involving integrals.)
consider the region r bounded by the parabola y=4x^2 and the lines x=0 and y=16 find...
consider the region r bounded by the parabola y=4x^2 and the lines x=0 and y=16 find the volume of the solid obtained by revolving R about the line x=1
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT