Recent content by yitriana

Homework Statement a) 8 new teachers are to be divided among 4 schools, and each teacher can teach at maximum 3 schools. There is a staff limit such that 3 of the schools only allow 4 new teachers. How many divisions are possible? The Attempt at a Solution Without staff limit a) So if...

Homework Statement The circular wire loop has 10 turns and a radius of 1.0 cm. The total electrical resistance of the 10 turn loop is 0.10 Ω. The magnitude of the magnetic field due to the solenoid near the wire loop at t = 0 s is 0.002 T. The current through the solenoid doubles between t = 2...

Homework Statement Find the points where the equipotential line is tangent to the thick black line Homework Equations The Attempt at a Solution I thought that it was A, G and K, because there, the electric field is horizontal and thus perpendicular to the black line and electric...

is it even possible to compute the curl of F of in terms of spherical coordinates in the cartesian basis, or would you have to convert F to spherical basis if F is in terms of spherical coordinates to compute the curl? (of course, the curl of F could be computed in cartesian basis in terms of...

I used spherical coordinate parameters but wrote in terms of x, y and z (cartesian coordinates). Ah. I figured out my mistake now. Since I did not rewrite F in spherical coordinates, I *cannot* take the curl with del as <d/dr, d/dtheta, d/dphi>--that would not work since F was expressed in...

Oh sorry. I was parametrizing in spherical coordinates but not necessarily using spherical basis vectors, which explains why I took the curl in cartesian coordinates (and did not need scale factors)

Homework Statement Suppose we want to verify Stokes' theorem for a vector field F = <y, -x, 2z + 3> (in cartesian basis vectors), where the surface is the hemispherical cap +sqrt(a^2 - x^2 - y^2) The Attempt at a Solution Why is it that if I substitute spherical coordinates x =...

I can't quite understand why this occurs. When a person is standing on insulating stool, and holds a large metallic sphere, which is charged with generator, why is it safe for him to do this? Why is it unsafe for another person to touch the sphere after it has been charged? My guess is...

How can the theory of metapopulations be related to Island Biogeography theory? Can we treat each population in a metapopulation as an island? Further, what is the significance of metapopulations anyway? Is it that they are more stable than individual populations themselves, since...

What is the best approach? I am considering taking the caltech transfer exam. What would be the most effective way to prepare?

How does one go about solving the first and second problems of this quiz? http://www.wiziq.com/online-tests/3503-algebra-iit-jee

Why is the angle between products in non head on, perfectly elastic collisions always 90 degrees?

\int_{r = 0}^{1} \int_{\theta = 0}^{2 \pi} (1 - r^2) r^4 (\cos(\theta))^2 (\sin(\theta))^2 d\theta dr

sorry, it is meant to read x = 1 - y2 - z2

Homework Statement Find \int\int\int y^2 z^2where E is the region bounded by the paraboloid x = 1 - y22 - z2 and the plane x = 0. The Attempt at a Solution The region is a paraboloid with vertex at x = 1, y = 0, z = 0. I chose z bounds to be between 0 and 1 - y22 - z2 for first integral...