Hi,
Adiabatic, iosbaric and isochoric processes are good approximations for a lot of thermodynamic phenomena in every day life.
But the conditions for a process to be isothermal are so artificial that i have grave difficulties to fudge a story.
Are there any examples of thermal...
Thank you for your fast and detailed answer! That supports my assumption that several authors leave the reader deliberatly (or not) behind some serious issues :uhh:
Now my thoughts about this are about to come to maturity...
Any other suggestions are appreciated as well =)
Hi,
isn't it a bit dangerous to claim that
\left[ x \cdot \left( \psi(x,t) \, \frac{\partial \psi^\ast (x,t)}{\partial x} + \psi^\ast(x,t) \, \frac{\partial \psi(x,t)}{\partial x} \right) \right]_{x=-\infty}^{x=\infty} = 0
for example?
Expressions like this one are often found in...
Biot-Savart's law can handle open ends, but there exists no vector potential for non closed currents (since it's not physical). For non closed currents the vector potential diverges.
For such an unsymmetric problem, where no closed current flow exists it would be the best to solve Biot-Savart's equation for discrete points (if possible) or numerically. I don't think, that a analytical solution exists!?
In addition i don't want to waste hours/days to solve an integral...
Hi,
i like the problems/exercises in the book
Physics for Scientists and Engineers, Lawrence S. Lerner, Jones & Bartlett Publishers
i think they teach good the physics behind the exercises, though only the solutions of the odd numbered problems are given. In addition they only take calculus...
Another possibility to convince you: how much is the acceleration of an object if the energy flow (Power) on it is constant? (as one dimensional treatment)
P = v(t) F(t) = m v(t) a(t) = m v(t) \dot v(t) = \frac{m}{2} \frac{\mathrm d}{\mathrm dt} \Bigl( v^2(t) \Bigr)
integration of both sides...
The connection between the force exerted on an object and the power which is dissipated is
P = \frac{\mathrm dW}{\mathrm dt} = \frac{\mathrm d}{\mathrm dt} \Bigl( \int \mathrm dt ~ \frac{\mathrm d\vec r(t)}{\mathrm dt} ~ F(\vec r,t) \Bigr) = \vec v \cdot \vec F
Maybe it is helpful for you to...
i guess you have the average power in mind!? The power the motor must provide at any time is
P = \frac{\mathrm dW}{\mathrm dt} \qquad \mbox{with} \qquad W = \int \mathrm dr ~ F = \int \mathrm dt ~ v(t) \, F
(i treat the problem as one dimensional) so
P = \frac{\mathrm dW}{\mathrm dt} = \int...
Maybe you know that the electric field is crucial for your consideration!?
I know that's slightly abstract, but the energy is not stored in the capacitor itself. It is stored in the electric field (only the sources and sinks of the electric field are located on the capacitor's plates).
In...
Are you used to the formula of the energy stored in an electirc field
W = \frac{\varepsilon_0}{2} \int \limits_\mathcal{V} \mathrm dr^3 ~ \vec E^{\, 2}(\vec r)
?
you're right
\hat r = \frac{\vec r}{|\vec r^{\,}|} \qquad \Leftrightarrow \qquad \hat r \cdot |\vec r^{\,}| = \vec r
this applied to the primary equation yields
\phi (\vec r) = \frac{1}{4\pi\varepsilon_o} \frac{\vec p \cdot |\vec r^{\,}|\hat{r} }{r^3} =...
You might expand the fraction with |\vec r|!
This yields
\phi (\vec r) = \frac{1}{4\pi\varepsilon_o} \frac{\vec p \cdot |\vec r^{\,}|\hat{r} }{r^3}
Maybe you cope with this!?