Recent content by Momentous

For the first one, my only guess is writing it as a function of x, x', and t. So I'd think that L = (ax^2, 2ax, t) Is that right?

Homework Statement So we have started Lagrangian Mechanics in my class, and I really don't understand it at all. My teacher keeps doing the math on the board, but he hasn't really said what a Lagrangian is, and what an Action is. I really am lost from the start with these problems. Any help...

I can't say that I know what that method is. Isn't my method using the E.dl form?

Homework Statement A point charge q is at the center of an uncharged spherical conducting shell, of inner radius a and outer radius b. How much work would it take to move the charge out to innity? (find the minimum work needed. Assume charge can take out through a tiny hole drilled in...

The only thing I'm worried about is that the question specifically says to write down a first order ODE, but I guess it doesn't make much sense in this case. So how do I take a time derivative of that? I'm a little confused because of the (dx/dt)^2 I'm guessing I want kx + ma = 0 wouldn't the...

Wouldn't that set up yield this... dx/x = ±sqrt(k/m)*dt and if you integrate... ln(x) = ±sqrt(k/m)*t I don't know much about eulers identity, but what if I took an exponential of that answer. Then it'd be x = e^[±sqrt(k/m)*t] which (and I know this part is wrong) I'd write as x =...

Homework Statement Consider a mass connected to a spring of stiness k. (a) Use conservation of energy to write down a first order differential equation obeyed by the mass. (b) Find the time t for the mass to move from the origin at t = 0 out to a position x assuming that at t = 0 it has...

Oh alright, that makes a lot more sense Is that second problem basically the same as testing for exactness in ODE?

hmm ok, so then if I took the negative gradient of that dot product, I would assume that I would get E = -C(x)v(x) - C(y)v(y) - C(z)v(z) when taking the derivative of the position vector. Unless it's not a time derivative, then I guess I would just leave it once I put in the gradient notation...

Well I guess the dot product in Cartesian is just C(x)r(x) + C(y)r(y) + C(z)r(z) From that, I would do E = -∇V, if that makes any sense. For the second problem, I'm not really sure what you mean by that. I know that you can integrate to find V, but again I'm not really sure how I can do that.

Homework Statement 1st Problem (a) Consider the electric potential V = C . r, where C is a constant vector. Find the electric field E(r). (b) For a given uniform electric field E = E(0)z^, using part (a) find the electric potential for this electric field...

Oh yeah, I should probably mention this too. It goes w/o saying, but there is a charge located at (0, 0, z0) as the initial condition.

Homework Statement Consider a sphere centered at origin with radius R > z0. By calculating the total flux ϕ = ∫E . da through the sphere, explicitly show that ϕ = q/ϵ0 Homework Equations Gauss's Law The Attempt at a Solution I have a general idea of what to do, but I just want...

I don't want to sound like I'm making excuses, but my Vector Calc skills are minimal at best. Most of my physics classes haven't made much use of applying calculus. We usually don't go into it that much. I know these are things that I should know, but most of it I don't. Vela, I imagine that...

Alright, so with the information you guys have given me, I think this is the closest I can get. (a.(v x r))' = a'.(v x r) + a.(a x r) + a.(v x v) by product rule Rewritten (a.(v x r))' = a'.(v x r) + a.(a x r) Rewrite as (a.(v x r))' = a'.(v x r) + r.(a x a) from the link that Simon...