Recent content by kuruman

To begin with, your expression in step 4 is dimensionally incorrect. All terms in the sum must have dimensions of length because ##d\mathbf r## is a length increment. The term ##\phi\hat{\boldsymbol{\phi}}## is dimensionless and, therefore, does not belong. To see what is correct, just draw a...

Thank you for your contribution. Please note that it is highly unlikely that you will get an answer to your query because this thread was initiated more than two years ago and @chiyu has not been seen here since then.

I am not sure what is being asked here. Is it Assume that the inner surface charge distribution is "pasted" on a shell of radius ##2a##. Find the electric potential at point P ? If so, I would consider the brute force method. 1. Find the electric field at point ##\mathbf r## from the center of...

Imagine a plane rotating like a turntable about an axis perpendicular to it. A line is drawn on this plane from the axis of rotation radially out. The plane is frictionless and you are in a car that has four thrusters, front, rear, right and left. Firing the front thruster moves you backwards...

My thanks to all those who honored me with their vote. It has always been a pleasure to contribute to PF and I feel privileged to be among good people. Yes, (s)he did. As soon as I saw his first few posts, I immediately thought to myself, "this is top new member material." Congrats...

I am very sorry, Robert, to hear about his passing. He was a valued member of this community, widely appreciated for his thorough, insightful posts and his sense of humor. He is sorely missed. Thank you for letting us know - we appreciate your thoughtfulness. You have my sincerest condolences.

It's the end of the year and once again I wish to thank the mentors and admins for their stedfast commitment to the PF cause and for cultivating a friendly yet professional milieu. I confess to having subscribed to a handful of social media in my past all of which I dropped due to a net...

And is reminiscent of other illustrious Armenians, such as Valedictorian, Hamiltonian, Lagrangian, ##\dots##

You mean something like this which is a paraprosdokian, or did you have a double-entendre in mind?

Correct. Putting this together with what @Ibix already mentioned, namely that light travels at the speed of light in all reference frames, if you travel at zero km/s relative to the speed of light, there can be no reference frame in which you will be "perfectly still." Does this answer your...

Think this through. If you are traveling at zero km/s relative to the dog you are walking, this means that you are moving at the same velocity relative to the ground as the dog. If you are traveling at zero km/s relative to a jogger, this means that you are moving at the same velocity relative...

Speaking of which . . .

Choice (B) is a bit ambiguous. To go to extremes, Tellurium-128 has a half-life of ##7.7\times 10^{24}## years via double beta decay. If I am given a sample, I "know" theoretically that it has started to decay but, arguably, the sample "has started to decay" as soon as I observe the first decay...

A figure sure helps.

OK, let's backtrack and write some equations. For part (a) you can write $$\mathbf E=\left[\sin\left(t+\frac{\pi}{4}\right),\sin(t)\right].$$ A parametric plot gives the figure on the right which is what you have shown in post #3. What equations will you get if you line up: 1. The quarter-wave...