Recent content by Kelvin

This is a homework problem of a EM course: Calculate the potential energy, per ion, for an infinite one-dimensional ionic crystal, that is, a row of equally spaced charges of magnitude e and alternating sign. Hint: The power series expansion of ln(1+x) may be useful. Here's my...

so putting x=\pi, \pi^4 = \frac{\pi^4}{5} + \sum_{n=1}^{\infty} \left( (-1)^n \frac{8(n^2\pi^2-6)}{n^4} (-1)^n \right) \frac{4\pi^4}{5} = \sum_{n=1}^{\infty} \left( \frac{8(n^2\pi^2-6)}{n^4} \right) \frac{4\pi^4}{5} = 8\pi^2 \sum_{n=1}^{\infty} \frac{1}{n^2} - 48...

I think you shouldn't depend too much on the derived formula in the textbooks. Try to derive the formula base on the theory you learn. I have drawn a diagram for you. I hope you can try again before reading my solution. the first thing we can write down is the snell's law: n_a \sin a' =...

to deal with the integral \int \frac{1}{(z^2+x^2)^{3/2}} dx try putting x = z \tan\theta and using the identity 1+\tan^2\theta = \sec^2\theta

I think I really made a mistake. The Fourier series of x^4 should be: x^4 = \frac{\pi^4}{5} + \sum_{n=1}^{\infty} \left( (-1)^n \frac{8(n^2\pi^2-6)}{n^4} \cos(nx) \right) then put x = \pi, the result follows

I am not sure I am 100% correct but what I got is slightly different from what we need. We have \sum_{n=1}^{\infty}\frac{1}{n^2} = \frac{\pi^2}{6} If we consider the Fourier series of f(x)=x^4 x^4 = \frac{\pi}{5} + \sum_{n=1}^{\infty}(-1)^n \left( \frac{8 \pi^2}{n^2} - \frac{48}{n^4 \pi}...

thanks a lot, OlderDan and PBRMEASAP! :rofl: thanks! the applet is very useful coz i don't have mathematica in my computer. I will try each method very carefully. actually i am not sure whether it is a book problem or a homework given by a professor. i am self-learning lagrangian...

I am trying to solve the following problem: A particle of mass m is constrained to move under gravity with no friction on the surface xy=z. What is the trajectory of the particle if it starts from rest at (x,y,z) = (1,-1,-1) with z-axis vertical? The lagrangian is...

but this question is an exercise in chapter 2 of "Introduction to Electrodynamics" ... how come I need tensor to solve the problem...

I don't know tensor... is there no other way to do this problem?

\[ \begin{gathered} {\text{OK, so I}}{\text{ try to start with potential, which is easier, then obtain the electric field by}} \hfill \\ E = - \nabla V \hfill \\ {\text{and finally }}F = qE.{\text{ So the potential at the point }}\left( {{\text{x}}_{\text{0}} ,y_0 ,z_0 }...

Find the net force that the southern hemisphere of a uniformly charged sphere exerts on the northern hemisphere. Express your answer in terms of the radius R and the total charge Q [the "model" answer is \frac{1}{4 \pi \epsilon_0} \frac{3 Q^2}{16 R^2}] my attempt: regard two hemispheres...

A few months later, I will have a choice between "theoretical physics stream" and "applied physics stream". but i don't know which one is more suitable for me. In high school, I would definitely choose theoretical stream coz I hated doing experiment so much. But after one semester in...

oh I got it correct thanks a lot my "picture of engine" is completely wrong ...

oh...I've found the answer :D so...let me redo the problem