Recent content by Helmholtz

Thank you for the reference paper, I found that to be a great help. I believe I now understand what the answer is, as derived in the paper.

Suppose you are given an incompressible material with a constant charge density. What shape would create the largest electric field at a given point in space? These seems like a calculus of variation problem, but I am wondering if there might be any clever trick. $$\vec E = \frac{\rho}{4 \pi...

Thank you. I looked over the integral again and see exactly what you are saying and better understand all of that work. I think I now understand. Here is where I see the 1/2 coming into play: $$\sum_{i,j} \int_1^2 \vec F_{ji} \cdot d \vec s_i = -\frac{1}{2} \sum_{i,j} \int_1^2 \left( \vec...

That looks right to me. I should note that in LaTex you can write time derivatives using the \dot, e.g., $$\dot r.$$ For higher time derivatives just put as many 'd's as there are time derivatives, e.g., \dddot r is : $$\dddot r.$$

The second term is taking into account that the radius can vary in time. Use the chain rule. You can also see that your second term doesn't have the right units, and you need a second time derivative somewhere.

I am following along with Goldstien's Classical Mechanics Book and I am on page 11. The text is breaking down the total potential energy of a system into two parts: the external conservative forces and the internal conservative forces. My question pertains to the internal forces. Writing the...

I have figured it out, thanks DrClaude.

Homework Statement Hello, maybe this is due to my lack of understand of RK4, but I have an equation: x'' + b^2*x=0 (derivatives with respect to variable t) and I need to use RK4 to find the solution on an interval. I can readily find solutions analytically, but my understanding of RK4...

Does this make sense to you now then? I was trying to imagine a circuit in which they could still be in parallel after disconnecting, but it would only lead to a short circuit such as: ...... ...____________... ..|...|...|... ..V...|...__|___... ..|...|...|...|... ..|...|...C_1...C_2...

Even when you disconnect them from the battery? I was thinking of a circuit like this: ...... ...__________... ..|...|... ..V...__|___... ..|...|...|... ..|...C_1...C_2.. ..|...|_____|... ..|...|... ..|__________|... ...... And then when you disconnect the battery it's in series in the square.

Thanks for the response. I have done that, but I didn't like what I did and I was wonder if this was something someone could confirm. Two forces directed in the same direction, one on top of the wheel, the other on the bottom. Forces add as such: F_1+F_2=ma (F_1 is the tension, F_2 is the...

I misread the question. I think it might be helpful to find the total charge placed on both capacitors. Then we know that this is the charge in the circuit after the battery is also disconnected. Then with the fact that capacitors in series have the same charge as one another it would be...

The charge on the capacitors do not change when you insert a dielectric. So as the capacitance goes up, the voltage goes down proportionally. So V_2 = V_0/k and C_2 new = C_2 * k Q_1=C_1 * V Q_2 = C_2 * V E_1 = V/d E_2 = V/(k*d) I think these are right.

Homework Statement A beam of particles of energy E = 9 eV strikes on a step potential and 25% of the beam's particles is reflected back. What is the height of the step potential? (A) 4 eV (B) 8 eV (C) 3 eV (D) 1 eV (E) 5 eV Homework Equations √(R) = [√(E)-√(E-U)]/[√(E)-√(E_U)] The Attempt...

Homework Statement A point charge +Q is placed at the center of a cube. What is the electric flux through a face of the cube? Homework Equations Flux = Q/ε The Attempt at a Solution The answer is Q/(4ε), but I thought it should be Q/(6ε) which isn't even an option. I'm I crazy? Since there...