Right, it would be in the opposite direction...but now I'm confused. Going by Gauss' Law, inside the sphere the E field will still be zero, won't it? Even with the little disk there's still no enclosed charge inside the sphere and therefore no E field...
I know the equation I have for the sphere contribution only works outside of the sphere, because the electric field inside a (normal) uniformly charged sphere is zero. The field around the disk, though, I thought would look the same in both directions. That would make the Etotal in my initial...
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 field point is somewhere on the positive z-axis (so z could be...
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...
The flux through the top is positive, so subtracting the flux through the open circle from what I already had gives me an even larger negative number, -51000000pi.
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...
I wasn't asking which as in "which one?" I was stating the final answer from the triple integral, and checking that it should be the final answer for the problem. I wanted to be sure there wasn't a step after the integral I was missing. However, the answer I got (1280pi) is incorrect. The...
So using cylindrical coordinates, I integrate 5r over r, theta, and x. The integral over r gives 40, the integral over theta gives 80pi, and the integral over x gives 1280pi, which would be my final answer?
And thank you for the welcome. :)
How do I use cylindrical coordinates if it's not vertical, though? That was my first thought, but since the equation is x = y^2 + z^2 instead of z = x^2 + y^2 I wasn't sure how to write it out.
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...