Recent content by Monsterman222

I'll show you how to do this in SI units, instead of CGS. The question is to derive the Lorentz force law using Hamilton's equations and the Hamiltonian of a charged particle in the presence the vector and scalar potentials, ie. $$H=\frac{(\vec p-e \vec A)^2}{2m}+e V ,\;\;\;\;\;\;(1)$$ where...

Thanks for your help so far, but I'm still struggling with this one. From the representation of the Bessel function involving the integral, I still can't prove it. Looking at Bessel's differential equation: x^2 \frac{d^2 y}{dx^2} + x \frac{dy}{dx} + (x^2 - p^2)y = 0 we can take the limit of...

I am aware that Bessel functions of any order p are zero in the limit where x approaches infinity. From the formula of Bessel functions, I can't see why this is. The formula is: J_p\left(x\right)=\sum_{n=0}^{\infty}...

Homework Statement The problem is from Mathematical Methods in the Physical Sciences, 3rd Ed. Ch10, Sec. 10, Q4. My question is a bit subtle as I have actually figured out the problem, just that I don't understand my solution. The problem reads: 4) What are the physical components...

Awesome, thanks! I was able to get it without completing the square, just squaring twice qfter rearranging.

Hi, I was looking at the derivation of the equation for a hyperbola on Wolfram Mathworld. In one step, the webpage instructs you to "complete the square". It starts with: \sqrt{\left(x -c\right)^{2} +y^{2}}-\sqrt{\left(x+c\right)^{2}+y^{2}} = 2a and then says, "rearranging and completing...

Possibly, but I'm still thinking the book has an error. The formula we would be deriving would only work for specific curves. It would not work for any curve which does not have any spot where C1'(t) = 0.

Yes, I think you're right in interpreting the identity that way. I think the author must have made a mistake. Given that t is an independent variable, then x(t) (that is, C1(t)) is not an independent variable, so when the author writes \left(\frac{\partial y}{\partial t}\right)_{x}\;\...

Hi Fredrik, thanks a lot for the help! I'll make sure to post questions from textbooks in the homework section next time. I have a follow up question. I'm a bit confused by: \left(g\circ C_{3}\right)'(t). Since g is a function of two variables, does this mean: g' \left(C_{1} \left(t...

I'm trying to figure out Ch 4, Sec. 7, Q 25.c of Mathematical Methods in the Physical Sciences, 3rd Ed. It's not homework I'm working on since I'm not in school. Assume that f\left(x, y, z\right) = 0 If x, y and z are each functions of t, show that \left(\frac{\partial y}{\partial...