Recent content by msbell1

Ok, another follow up question. So I now know that the length of a rod as measured by inertial observers doesn't depend on the direction of ##\textbf{v}## as long as ##\textbf{v}## is perpendicular to the rod. If the purpose of the proof is to show in general that the spacetime interval between...

Thanks for the reply. I'm still a bit unsettled by this. I think my main hang-up is that this relationship between the lengths was obtained by assuming the rod was oriented perpendicular to the velocity of frame ##O'## relative to frame ##O##. I can see how the argument holds for any other...

Homework Statement From pages 10--11 in "A First Course in General Relativity" (Second Edition) by Bernard Schutz: Given $$\Delta\overline{s}^2 = \phi\left(\textbf{v}\right)\Delta s^2,$$ where ##\Delta \overline{s}^2## is the interval measured between two events in frame ##O'##, which is...

Homework Statement Integrate ∫dx/(sin(x)+a), where a is a constant.Homework Equations The Attempt at a Solution I have been working on this for a while, and for some reason I can't figure it out. The attempt that seemed the most promising to me was to multiply top and bottom by (sin(x)-a)...

I think it's kind of just an abstraction to make it easier to think about and solve problems. Really, the basic thing here is the force between two charges, given by Coulomb's Law. From that, we can begin to talk about an electric field (force per unit charge)---something that can exist with...

After thinking about this some more, I may have a lead on how to solve it. Some information I left out that I'm thinking is probably important is that the camera lens/objective has a focal length of 6.5 mm. I then used the simple lens equation to find the image distance (assumed object distance...

Here is the picture, by the way.

Homework Statement A diffraction grating with 500 lines per mm is held directly in front of the lens of a digital camera, with a bright white light source 8m away. The image recorded by the camera shows both the light source and the spectrum created by the light source. We know that the CMOS...

Thank you very much! I see that now! If I try this when q2 = -q1, I find x = [(1 (+or-) sqrt(-1))/2]*r. Since this is imaginary, I guess this indicates that there is no solution between q1 and q2 when their signs are opposite, which is true.

Homework Statement Two charges, q1 and q2, are separated by a distance r. Find the position at which a third charge, q3, can be placed so that the net electrostatic force on it is zero. Homework Equations Coulomb's Law: F = (kq1q2)/r122 * (r12hat) The Attempt at a Solution I was...

Thanks! I kind of see it now. Definitely I can see how these still satisfy commutativity and associativity for both addition and multiplication. Now if I focus on addition, I guess I need to define some scalar, I will call it 0*, such that a \oplus 0* = a (which implies that f(0*) = 0 where...

Homework Statement This question consists of three parts, the first two of which I have answered: a) Is the set of all positive integers a field? (positive indicates greater than or equal to 0, and ordinary definitions of addition and multiplication are being used) No. There is no additive...

Thanks a lot--especially for the outline!

Thanks for the reply! I forgot to include that multiplication is distributive with respect to addition: a(b+c) = ab + ac (which I will use later) Would it be ok to first rewrite (-1)a(-1)b as (-1)(-1)ab and then start working separately on the (-1)(-1) part? like continuing the proof as...

Hi, I am trying to work through Finite Dimensional Vector Spaces by Halmos, and I am having some difficulty with the first problem on page two (the specific problem is included below). The last class I took involving formal proofs was linear algebra about 8 years ago, and I am very rusty, but I...