Recent content by Potatochip911

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    Falling Rain Drop (Variable Mass)

    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 =...
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    Falling Rain Drop (Variable Mass)

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

    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...
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    I Stuck on the probability of rolling 'p' with 'n' s-sided dice

    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...
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    I Stuck on the probability of rolling 'p' with 'n' s-sided dice

    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) =...
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    Find B and H everywhere for a magnetized infinite cylinder

    Thanks! This pieces everything together.
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    Find B and H everywhere for a magnetized infinite cylinder

    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...
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    Find B and H everywhere for a magnetized infinite cylinder

    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...
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    Find B and H everywhere for a magnetized infinite cylinder

    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}##...
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    Electric field inside a uniformly polarized cylinder

    Am I drawing it incorrectly? I still don't find the same result as you.
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    Electric field inside a uniformly polarized cylinder

    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...
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    Drawing a Timing Diagram

    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##
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    Drawing a Timing Diagram

    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...
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    Calculating the surface charge of a sphere and a conducting shell

    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?
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    Calculating the surface charge of a sphere and a conducting shell

    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...
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