I'm attempting to figure out the total current induced in a hollow metal tube as a result of the EMF due to a constantly varying magnetic flux through its cross-section.
Faraday's law of induction states that for an infinitely thin loop of wire in such varying magnetic flux has induced EMF...
My issue is that I don't see what prevents a spaceship throwing off fuel at a constant rate A kg/s, so that:
\frac{dp}{dt} = \frac{GMm}{r^2}
A v = \frac{GM(m - At)}{r^2}.
What prevents this system (classically, so long as v is not too large) from escaping the event horizon?
My...
When classically deriving the Schwarzschild radius of a black hole, the kinetic energy of an outgoing particle (moving at the impossible-to-achieve maximum of the speed of light) is equated with the gravitational potential of the black hole at that point.
\frac{1}{2}mc^2 = \frac{GMm}{r}...
In van der Waals' equation for real gases, the adaptation to account for intermolecular attractions in real gas is a\frac{n^2}{V^2}. This implies that the pressure due to the VDW forces on the container is proportional to the square of the density, \rho^2 = \frac{n^2}{V^2}.
When I do...
So what would happen to other energies, such as kinetic energy? Let's say two antiparticles collide with certain velocities, v; where would their KE manifest itself after annihilation?
If a particle has a certain potential energy then collides with its antiparticle, releasing energy according to E=2mc^2, what happens to the PE of the two particles?
Let's say that a particle has a gravitational potential energy of X, wouldn't the antiparticle need to have a GPE of -X in...
You raise a very good point. The dipole-dipole force falls off as \frac{1}{r^3} only along the plane equidistant between the two poles. Doh.
As far as the LDF intermolecular forces go, the attraction is entirely independent of direction and therefore spherically symmetrical.
To my knowledge there existed a fair amount of forces that are not inverse-square in nature.
When electric dipoles are involved, for instance, the decay becomes one of \frac{1}{r^3}. Also, the macroscopic functions for intermolecular forces such as those due to dipole-dipole and Van der Waals...
I am curious as to whether the force of solid sphere can be considered to be originating entirely at its center when the force is not of \frac{1}{r^2} nature.
It is said that the field inside a uniform spherical shell is zero for any \frac{1}{r^2} type force and not for any others. It would...
Consider a sphere of mass M and radius R. The interior of the sphere is a uniformly distributed mass M.
The surface shell of the sphere has a certain mass dm. What is the pressure on the surface of the sphere due to gravitational forces?