Recent content by nos

Heey everyone, I was wondering how long it takes for a small mass to reach the Earth from infinity . The trajectory is completely radial, so it's a relatively simple equation. $$r''(t ) =\frac{ - GM} {r(t)^2}. $$ But what if we multiplied both sides by ##2r'(t) ##. Then it follows, $$2r'(t)...

I tried to solve the differential equations and solve for the total time in the air. In this graph drag constant and gravity is set to 1. The variable x denotes the lift off velocity. So yeah, I think you are right, especially at high speeds.

Heey all, Do you think it will take longer for an object shot from the ground vertically to reach to ground again with air resistance or without? Keep in mind, no air drag means it will go higher, but it won't be slower down on the way back.

Hey guys and girls, We have all stumbled upon some problems/tasks where We would have no idea how to proceed. (I am not talking about calculation errors). What works best for you in these situations? I usually go do something completely else. Activating Other parts of the brain may give you...

Oh right thanks, so the second last line is positive. I tried to simplify the answer a bit more and this is where I think made a mistake. Imagine a triangle with angle θ. \begin{align*} \theta=\arctan{\sqrt{\frac{k}{mg}}v_0} \end{align*} Then the opposite and adjacent sides are \begin{align*}...

This is the correct answer for the velocity function. I realized I missed a constant and instead \begin{align*} a=\sqrt{\frac{k}{mg}}\end{align*} So \begin{align*} v(t)=\sqrt{\frac{mg}{k}}\tan{\Big[\arctan{\Big(\sqrt{\frac{k}{mg}}v_0\Big)}-\sqrt{\frac{gk}{m}}t\Big]} \end{align*} Integrating...

Hello everyone, I was playing around with some equations regarding air resistance. I tried to calculate the height that is reached by an object that is projected vertically into the air. However something seems to go wrong when integrating. Starting with the equation of motion \begin{align*}...

Hello all, I want to prove the following inequality. sin(x)<x for all x>0. Now I figured that I put a function f(x)=x-sin(x), and show that it is increasing for all x>0. But this alone doesn't prove it. I need to show we have inequality from the start. I can't show that lim f(x) as x->0 is...

Ah I see now. Of course, the formula for B-field stays the same, but the current for slowly particles is lower than current produced by fast particles, thus a different value for B-field. Actually my question should have been: Is it true that the formula stays the same taking relativity into...

Hi there, Is it true that the magnetic field of a straight wire is the same when the charges are moving at low speeds (v <<c) as when they are moving at relativistic speeds (v~c). The extra relativistic factor the magnetic field gets from the moving charges cancels upon integrating. According...

Oh thans you, but I am interested in solving them tot get the Electric and magnetic field in terms of q(e) and q(m) and position, velocity and acceleration. I guess for each field you het two terms: because now both electric charge and magnetic charge create electric field and magnetic field.

I am referring tot point charges.

Hi all, Suppose magnetic monopoles exist, how would the maxwell equations be solved? Because the divergence of B is no longer zero, we can not use the vector potential, can we? Do you just solve for the electric and manetic field for electric charges and magnetic charges separately and then add...

oh I've got it. Forgot the minus sign in the triple cross product rule :$

Hi all, I was going through the derivation for the electromagnetic field of point charges by Griffith(Introduction to electrodynamics page 437). I'm missing minus sign somewhere: The book says that:\nabla(\vec{n}\cdot\vec{v})=\vec{a}(\vec{n}\cdot \nabla...