Recent content by raging

I see. Thanks for the comment! I guess something like X/(Y+1) this just becomes a vector calculus problem. But would you strategy work for non-continuous functions as well? For example, the step function or the min and max functions? How would we decide what g(x,y) is less than if that quantity...

Simple joint distributions such as X+Y are usually worked out in textbooks, but how would we approach a general case. For example, let X any Y be independent variables each defined on the interval [0,infinity], and having densities f(x) and f(y) respectively. How do we find, for example, the...

Hi, I'm currently a freshman still deciding my major. What is the best major if one wants to pursue medical research including antibiotics, drug design, cancers, and fields of other diseases. Is Chemical and Biomolecular Engineering a good choice? How about pure Biology or Biochemistry...

True. But to solve that surface integral simply one must apply a symmetry argument. How do you arrive about that symmetry? The induced charge will not be evenly distributed on the outside of the sphere, but is there a way to apply uniqueness to arguing that?

This is NOT a homework. Concentric cavities are too easy. I'm wondering if we can somehow apply uniqueness here to show that it actually doesn't matter where the cavity is...

Suppose we had an uncharged solid spherical conductor with radius R, and some spherical cavity of radius a that is located b units above R, where a+b<R. If we place a charge inside the cavity at the center, how would you quantitatively express the E-field lines outside of the conductor?