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What examples of a system can be described by a system of ordinary differential equations?
You're not far off, but there are a few key points to clarify. Hawking radiation is a result of quantum mechanics in curved spacetime and isn't predicted by general relativity alone. GR doesn't acc...
The incremental inductance depends on the natural log of the l/d ratio. It also is reduced by the gap of the return conductor but is not affected by the dielectric around it. https://www.mantaro.c...
Lets say we have a mass connected to a spring.Assuming not any friction the ODE which describes the system is $m\frac{d^{2}x}{dt^{2}} = -kx$ We can set 2 Dirichlet boundary conditions $x(0)=0$ an...
Suppose you have two photons A and B on an x, y plane: Photon A is at (-20, 9) and traveling towards (20, 0). Photon B is at (-20, -9) and traveling towards (20, 0). Both photons have waveleng...
Maxwell's first law in differential form states that $$ \triangledown \cdot E = \frac{\rho}{\epsilon_{o}} $$ . In case of 1d can we say that $$\rho = \lambda$$ where $$\lambda$$ is the linear char...
Gravitational waves can be derived from the non-linear Einstein field equations and since they are by definition waves they must obey the wave equation: $u_{tt}=c^{2}u_{xx}$ but in General Rela...
I'm trying to understand the uncertainty principle and its implications for particle measurement. From what I've read, it seems that the principle states that we cannot simultaneously know the exac...
Yes, that would the obvious interpretation of that equation in one dimension. Note also that in that case, the divergence also reduces to the ordinary derivative. In other words, in one dimension,...
$$\begin{alignat}{2} && \vec \nabla \cdot \vec D & = \rho_f \\ & \implies &\int_V \vec{\nabla} \cdot \vec D \mathrm d\tau & = \int_V \rho_f\ \mathrm d \tau \\ & \impl...
With time dilation a cosmonaut could travel forth in time, especially in light speed. But are there much lesser speeds which might be achievable by humans in the next 100 years which could also in...
Kinetic energy of any particle (who has mass) is $$T=\frac{1}{2} m\ddot{x}^2$$ OP had took potential as potential energy, that was wrong. $$U=-\int \vec F\cdot d\vec l $$ For the case, The forc...
No. A calendar or, more generally, a time measurement system, can be based on anything. While human calendars have (generally) been based on: Day = One cycle of the Earth's rotation Month = On...
We don't know the details of your setup, but most likely there was a partially reflective surface over the actual photoresistor. The photoresistor itself may also be partially reflective. A highe...
Let's start with displacement field equation $$\vec D = \epsilon_0 \vec E + \vec P$$ We know that $$-\vec \nabla \cdot \vec P = \rho_b$$ Here $\rho_b$ is surface charge density. $$\implies -\in...
The Euler-lagrangian equation gives the equations of motion that once solved give you a family of solutions that minimize the action. A unique solution is given by specifying boundary conditions....
I dont think anyone can make a universal calendar because time flows more slowly or more fast between different regions in the universe or it can even go backwards if you come close to a rotating b...
I have recently heard of Apsidal Vectors. I was searching about it through internet. I had found the video in YT. I had found similar question in PF. But, the PF answer wasn't clear to me. I am jus...
Laplacian acts like Divergence but not completely. If you take a function (called $\vec{A}$) and write that laplacian of that function is $0$ than it will be flat space. $$\nabla^2\vec{A}=0$$ But...
I was looking for equation of motion. I came up with a solution but it doesn't satisfy me. Cause I was trying to find motion of that particle using Lagrangian. We know that $$W=\int \vec F\cdot d\...
Which one is correct? $$E=mc^2$$ or $$E^2=(mc^2)^2+(pc)^2$$ I mostly seen $$E=mc^2$$ from my childhood, and when I was learning problem solving in relativistic mechanics I had seen $$E^2=(mc^2)^2...
Is it the correct time to have a moderator? It's already a year we have the Physics community. But it's really inactive. There's only 42 question in Q&A which proves that we still don't have l...
I saw following equation in Griffiths EM $$V(r)=-\int_\mathcal{O}^r \vec E \cdot d\vec l$$ While the surface was closed but not symmetrical circular. At first I was thinking $\mathcal O$ was repr...
How to derive the Lagrangian differential force? $$\frac{d}{dt}(\frac{\partial L}{\partial \dot{x}})+\frac{\partial L}{\partial x}=0$$ I was trying to do something. $$L=T-U=\frac{1}{2} m\dot{x}^...
For an absolute beginner : If you don't have any idea of any theories than, I would suggest to study theories at first. Just practice beginner problems at first which contains no-calculus(It's OK ...
