Recent content by Potatochip911

Yes it does thanks. Interesting for some reason I had it in my mind that they had to be polynomials. $$\frac{dv}{dt}+\frac{k}{m}v=g $$ $$\ln P(t)=\int \frac{k}{m_0+kt}dt=\ln{\left (m_0+kt\right )}+C $$ $$P(t)=e^C(m_0+kt)$$ $$\frac{d}{dt} ( v(m_0+kt)e^C ) = (m_0+kt)e^Cg$$ $$v(m_0+kt)-v_0m_0 =...

$$mg = \frac{d}{dt}(mv)$$ $$d(mv) = mg\cdot dt$$ $$\int_{t=0}^{t=t} d(mv) = g\int_0^t(m_0+kt)dt$$ $$mv-m_0v_0 = g(m_0t+kt^2/2)$$ $$v = \frac{m_0v_0+g(m_0t+kt^2/2)}{m_0+kt}$$ Their expression for velocity is so simplified in the paper I can't even tell if this is correct. I have basically no...

I was looking through my posts when I stumbled upon this one and I can't understand how they're solving the differential equation in the paper that was linked in response to this post. The author states that when ##\frac{dm}{dt}## is independent of velocity then the accretion equation can be...

I'm still finding this quite confusing. I understand what you're saying here that these are the boundaries for ##l## using ##k##. Then it seems like the last summation can be written as $$ \sum_{l=p-n}^{p-n-sn}\binom{p-sk-1}{p-sk-n}x^{p-sk-n} $$ but since ##l## has been replaced we also need...

Hi, I've been following the derivation of wolfram mathworld for this problem and I'm running into some trouble regarding the summation indices. Currently I am at the step where we have found that (it's pretty much just binomial expansion and taylor series to get to this point) $$ f(x) =...

Thanks! This pieces everything together.

Yes I agree that geometry doesn't make much sense to me either I was just copying what they had done. Setting up the problem as $$\vec{B}(2\pi s) = \mu_0(\int_s^a J_d\cdot 2\pi s\, ds - M_0\cdot 2\pi a) $$ results in the answer of $$\vec{B} = -\mu_0 M_0 (s/a)^2\hat{\phi}$$ which is just the...

Ok, the difference was in the book that their ##\vec{J_b}## was a constant so they could just multiply by the area to get the result of the integral however, my ##\vec{J_b}## is linear w.r.t. s although I am still running into trouble. Defining ##dA =l \,ds\Longrightarrow \int_s^a J_d\cdot dA...

Homework Statement An infinitely long cylinder of radius a has its axis along the z-direction. It has Magnetization ##M=M_0(s/a)^2\hat{\phi}## in cylindrical coordinates where ##M_0## is a constant and s is the perpendicular distance from the axis. Find the values of ##\vec{B}## and ##\vec{H}##...

Am I drawing it incorrectly? I still don't find the same result as you.

Homework Statement This is problem 4.13 from Griffiths. A long cylinder of radius a carries a uniform polarization P perpendicular to its axis. Find the electric field inside the cylinder. Homework Equations ##\int \vec{E}\cdot dA = q_{encl}/\varepsilon_0## The Attempt at a Solution [/B] We...

Hmm, now I'm confused because depending on whether or not I start at the top or bottom gate outputting 0 I will end up with either ##Q=1##, ##Q'=0## or ##Q=0##, ##Q'=1##

Homework Statement Draw the diagram for the following circuit given the following conditions: 1) X=Y=Z=1 2)X=Y=1, Z=0 3)X=Y=0, Z=1 4)X=1, Y=Z=0 Homework Equations The Attempt at a Solution [/B] ##W=XZ'+YZ##, ##V=Y'Z+XY## 1) W = 0 + 1 = 1 V = 0 + 1 = 1 and now I'm not sure how to get the...

So in an insulator the electrons can't flow freely therefore they won't be able to redistribute across the surface? Yes, is it just a conductor because it's metal?

I thought that charge only entirely resided on the surface of conductors otherwise why would they mention this as a property of conductors and not just in general? After looking around it seems like the charge will always distribute across the surface of anything in order to minimize the...