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Results tagged with homework-and-exercises
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user 208245
Applies to questions of primarily educational value - not only questions that arise from actual homework assignments, but any question where it is preferable to guide the asker to the answer rather than giving it away outright. Please READ THE GUIDANCE IN META before asking homework-like questions.
0
votes
Accepted
When is the approximation of neglecting the surface energy most useful during estimating the...
The total energy of the spherical system is
$$E=aT^{\frac {1}{2}}4\pi R^2+bT\frac {4}{3}\pi R^3=bT\frac {4}{3}\pi R^3(1+\frac {3a}{bR\sqrt {T}})$$
The second term in brackets will be small compared to …
- 3,794
0
votes
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Induced Current
When the switch is closed, then we have a current in the circuit and the corresponding vector potential $\vec {A}(x,y,z)$. When the switch is open, then with $t\rightarrow \infty$, the state $\vec {A} …
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1
vote
Accepted
Field Line Diagram for Small Bar Magnet in a Magnetic Field
The geometry of the lines depends on the magnitude of the external field. In fig. shows the case of a relatively weak external field.
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3
votes
How does the coil rotate?
Since all calculations did by hft actually is right, we only proposed picture for this question how coil looks like from three different point.
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1
vote
Accepted
Vector potential of a square loop
There are several papers about magnetic field of several rectangular loops discussed in my answer here including
M. Misakian, “Equations for the magnetic field produced by one or more rectangular loops …
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0
votes
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Time scale for steady flow to occur in parallel disk viscometer
To clarify the physical meaning of the characteristic time scale $t_0=R^2/\nu$, we consider the equations of fluid motion in the gap between the disks. In a cylindrical coordinate system $(r,\phi,z)$, …
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Complex Potential describing inviscid fluid flow
Let's pretend that this potential describes inviscid flow around cylinder with radius $r=\sqrt {2}$. We have $u = (4 - 8/r^2)\cos {\theta},v = -(4 + 8/r^2)\sin {\theta}$. Using the no-flow condition …
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vote
Mathematical Model for a Pendulum in an Electric Field
There is a simple 1D model that takes into account the force of gravity, the force acting on a charge in an electric field and the coefficient of recovery of the velocity of a pendulum upon impact. It …
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-2
votes
Accepted
Steady solution for flow in Boussineq approximation in star
We write the system of equations in the form
$$\dfrac{\partial v_{z}}{\partial t} = -\dfrac{1}{\rho_0}\dfrac{\partial \delta P}{\partial z}+\alpha g \delta T\quad(1)$$
$$\dfrac{\partial v_{x}}{\parti …
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3
votes
Accepted
Accurate Equation for Earth's Gravitational Binding Energy
To calculate the gravitational energy should use two integrals
$M(r)=4\pi\int_0^r\rho(r')r'^2dr'$
$U=4\pi G\int_0^{R_E}\rho (r)M(r)rdr$
$R_E=6.371×10^6 m$
We use the density distribution obtained …
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How would the path of a satellite be affected by the gravitational constant decreasing?
To confirm the hypotheses published by Maury and Elio, we consider the satellite motion model, in which we set $G(t)=1-t/100$
$x''(t) = -G(t)x(t)/(x^2 + y^2)^{3/2}$,
$y''(t) = -G(t)y(t)/(x^2 + y^2) …
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6
votes
How do we find the equation for the gyrating motion of a particle in a uniform magnetic fiel...
The equation can be integrated once, then we have second order equation
$$x''+x'+\frac {x^2}{2}=C_1$$
Make a substitution $x'=y(x)$, then $x''=y\frac {dy}{dx}$ as a result, we obtain the Abel equation …
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20
votes
Shape of a rotating rope with one free-end
Before developing the theory, I decided to first make an experiment in order to understand, what we are dealing with. A cylinder with a diameter of 11.5 cm is mounted on the motor shaft (I used an old …
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