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1. ### Charged Sphere with a Hole - Check my work?

Charged Sphere with a Hole -- Check my work? Homework Statement You have a spherical shell of radius a and charge Q. Your sphere is uniformly charged except for the region where θ<= 1° (which has σ = 0). Imagine that your fi eld point is somewhere on the positive z-axis (so z could be...
2. ### Linear, second-order differential equation?

One of my homework problems this week was: Verify that y = sin(4t) + 2cos(4t) is a solution to the following initial value problem. 2y'' + 32y=0; y(0)=2, y'(0)=4 Find the maximum of |y(t)| for -infinity< t < infinity. Verifying that the given y equation is a solution is easy, all...
3. ### Flux through a paraboloid?

The Problem: I have a paraboloid open along the positive z-axis, starting at the origin and ending at z = 100. At z=100, the horizontal surface is a circle with a radius of 20. Water is flowing through the paraboloid with the velocity F = 2xzi - (1100 + xe^-x^2)j + z(1100 - z)k. I'm asked to...
4. ### Using the Divergence Theorem to Find Flux

Let W be the solid bounded by the paraboloid x = y^2 + z^2 and the plane x = 16. Let = 3xi + yj + zk a. Let S1 be the paraboloid surface oriented in the negative x direction. Find the flux of the vector field through the surface S1. b. Let S be the closed boundary of W. Use the Divergence...