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The electrons by themselves don't absorb or release this energy. They do that within the context of the atom they are within. The discrete energy levels available to electrons are only there due ...
In classical physics book of kleppner, i read that An atom can "jump" from one stationary state a to a lower b by emitting radiation with $E_a-E_b$. The frequency of the emitted "package of radi...
The spring constant specifies force per compression distance. When you put multiple spring in series, the force on each spring is the same, which is also the overall force on the combined spring. ...
I know that equation for parallel resistance is $$\frac{1}{r_{tot}}=\sum_i \frac{1}{r_i}$$ But i wonder to see equation of series spring constant. If we add multiple spring in series. Then their ...
That sounds like something I'd say, so I'll explain this from my point of view, in particular regarding 'relativistic mass'. An 'outdated' theory or piece of terminology isn't typically mathematic...
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. $$\implies -\in...
$$\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...
I was recently reading some questions here and there saying that "relativistic mass is outdated". I saw someone saying that "outdated" doesn't mean the concept is wrong. My question is what physici...
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 $$W=\int \vec F\cdot d\...
This looks like a typical halogen light bulb. They are: Extremely hot Very bright Very small The combination means that, until bright, efficient and affordable white LEDs came along (LEDs h...
I'd say it's not the best design. Maybe that's why they discontinued it. However, there are also advantages. Cooling will be a little easier without a cover. But the real advantage is price. U...
IKEA discontinued this NOVEMBER lamp in 2007, but I still use it. IKEA confirmed that they did not intend or design any cover or share with this lamp, and the light bulb is supposed to be exposed. ...
Change in momentum is force times time. On the other hand, change in kinetic energy is force times distance (more accurately, the component of the force along the movement times distance; a force p...
Your analysis seems pretty good. To take an equivalent but more traditional example, imagine we throw a ball upwards. Ignoring air resistance and approximating the gravitational force as constant, ...
In short, momentum is vector and kinetic energy is scalar. $$\vec p = m \vec v \tag{1}$$ $$T = \frac{1}{2}m \vec v^2=\frac{\vec p }{2m} \tag{2}$$ Two momenta in opposite direction is $0$. Total ...
Momentum is proportional to an object's velocity, and kinetic energy is proportional to the square of its velocity $\dfrac{mv^2}{2}$. It's pretty intuitive that if object B is going twice as fast a...
I will use $m_0$ for rest mass in the answer and $m$ for relativistic mass. The main equation is, $$E^2=(m_0c^2)^2+(pc)^2$$ Here momentum is relativistic hence $p=\gamma m_0 v$ $$=(m_0c^2)^2+(\g...
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 $$E^2=(mc^2)^2...
After 4 edits, it seems you are asking whether there are places in the universe where galaxies can form, but planets in those galaxies can't support life. It seems you want life to be impossible d...
As you probably know, one of the postulates Einstein's Special Relativity is based on is that all observers see light in vacuum go at the same speed $c$. Now consider a lamp at rest relative to Jo...
All given metrics are for orthonormal-basis. 2 dimensional spacetime : I saw that Minkowski Metric looks like this : $$\pmatrix{-1 & 0 \\ 0 & 1}$$ or $$\pmatrix{1 & 0 \\ 0 & -1}...
Are there areas in the observable universe which surely cannot contain galaxies with planets that can support life as we know them?
To understand virtual work you should understand virtual displacement first, The wiki I have linked in first paragraph describes virtual displacement deeply. Usually we write $\delta$ or $d$ to sa...
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...
Actually $\mathcal O$ is some standard point and $r$ is where potential depends on. $$V(b)-V(a)=-\int_{\mathcal{O}}^B \vec E \cdot d\vec l +\int_{\mathcal{O}}^A \vec E \cdot d\vec l $$ $$ =-\int_{...
