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    MHD problem

    Yeah Faraday's law holds, so maybe \frac{\eta}{\mu_0} \nabla^2 \vec{B} - (\nabla \cdot \vec{v})\vec{B} - \frac{\partial \vec{B}}{\partial t} = 0 is a correct answer? But what about the behaviour of the field lines? Could one say that for high resistivity the current is zero and the magnetic...
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    MHD problem

    Homework Statement Two of the MHD equations can be formulated as \vec{E} + \vec{v} \times \vec{B} = \eta \vec{J} \nabla \times \vec{B} = \mu_0 \vec{J} where [itex]\eta[/tex] is the resistivity of the plasma. a.) Derive an equation for the magnetic field at very high resistivity and...
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    Show that a longitudinal wave is electrostatic

    Sometimes I feel so smart that I dunno what to do with myself. ;) Thanks!
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    Show that a longitudinal wave is electrostatic

    I tried with \vec{B} = B_0 \sin{[i(kx-\omega t)]} so \nabla \times \vec{E} = i \omega B_0 \cos{[i(kx-\omega t)]} But that doesn't really help me.
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    Show that a longitudinal wave is electrostatic

    Homework Statement Show that all longitudinal waves must be electrostatic by using Faraday's law. Homework Equations Faraday's law: \frac{\partial \vec{B}}{\partial t} = - \nabla \times \vec{E} The Attempt at a Solution Where should I start??
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    Solar wind at jupiter

    Homework Statement I'm trying to solve a problem related to the solar wind pressure at jupiter but I'm stuck at calculating the density. It is stated that the solar wind has a density of 5 [itex]cm^{-3}[/tex] and a speed of 400 km/s at the orbit of the Earth, and that it should be assumed...
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    Plasma MHD

    Homework Statement Two of the MHD equations can be written as \vec{E} + \vec{v} \times \vec{B} = \eta \vec{J} \vec{\nabla} \times \vec{B} = \mu_0 \vec{J} where [itex]\eta[/tex] is the resistivity of the plasma. Derive an expression for the magnetic field at a very high resistivity...
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    Plasma physics

    Homework Statement Derive (from the equation of motion of a neutral gas and an assumption of constant gravitational field) an expression showing why the concentrations of neutral molecules decrease approximately exponentially with increasing altitude, and why the concentration of atomic oxygen...
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    Complex integration

    Got it, so w(x) = \int_{-u_0}^{u_0} i2 \pi v e^{i2 \pi vx} dv = \frac{1}{\pi x^2} \left[ 2 \pi u_0 x \cos{(2 \pi u_0 x)} - \sin{(2 \pi u_0 x)} \right]
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    Complex integration

    \int f(v) e^{iavx} dv = \int f(v) \left( \cos{avx} + i \sin{avx} \right) dv = = \int f(v) \cos{avx} dv + i \int f(v) \sin{avx} dv Maybe?
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    Complex integration

    How do I solve an integral of the type \int f(v) e^{iavx} dv ? Can I just treat i as any other constant?
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    Rayleighs per count for a CCD

    I'm using that paper, my problem is that I'm not really sure about the definition of counts.
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    Rayleighs per count for a CCD

    How can I find the number of Rayleighs per count if I know the column emission rate, radiance, irradiance, #photons per pixel and #photoelectrons per pixel? I'm totally lost in this one, please help!
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    Time varying heat conduction

    Hey everyone! I am currently on a project building a small CanSat. This is a small satellite of the size of a coke can which will be launched together with a balloon and then descend from an altitude of 35 000 m. My problem now is to work out the heat conduction to see if our insulation is...
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    Determine the force in z-direction on the gyrocenter of a charged particle

    I did it with the Lorentz Force on the guiding center and got the equation given by Astronuc but with a plus sign. I guess that the sign is dependent on the charge.
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    Wavelength of particle motion

    I thought about that too, but it's stated in the problem that the motion is periodic with period \Omega. Anyway, my question still remains.
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    Wavelength of particle motion

    I have two parametric equations for the speed of a particle in a plane: \dot{x}(t) = A \left( 1 - cos{\Omega t} \right) \dot{y}(t) = A sin{\Omega t} The period is equal to \Omega. How do I find the wavelength of the motion? The wavelength is just \lambda = \Omega v , where v =...
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    Determine the force in z-direction on the gyrocenter of a charged particle

    Homework Statement Determine the force in z-direction on the gyrocenter of a charged particle in a diverging magnetic field. \frac{\partial B}{\partial z} < 0 Homework Equations The Attempt at a Solution Please give me a starter. Could I use the Lorentz force in this case?
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    Orbit calculations

    Homework Statement The given data is the perigee altitude r_p, the apogee altitude r_a and the period T. Mission: find the altitude 30 min after perigee passage. Homework Equations Semi-major axis a is calculated. Kepler's equation gives a relation for the eccentric anomaly E: E -...
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    Root loci

    Homework Statement For the double integrator described with transfer function G(s) = \frac{1}{s^2} the initial condition is zero. The double integrator is subjected to a unit‐feedback system where the controller is chosen as 1) a PI-controller with C(s) = k_p \left( 1 + \frac{1}{s}...
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    Control theory

    Homework Statement I have a transfer function G(s) = \frac{1}{s^2} and a PI controller P(s) = 6 \left( 1 + \frac{1}{s} \right). How do I check for stability? Just use 1 + P(s)G(s) = 0 and check the roots?
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    Gauge transformations in GR

    ? I have an expression for a gauge transformation for scalars: \bar{Q}(x^{\mu}) = q(x^{\mu}) - \xi^{\nu}\partial_{\nu}Q[/tex]. This gives the transformation for the scale factor as above. Then I have the transformation for the matric which gives the above expression for h_{\mu\nu}, but how...
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    Gauge transformations in GR

    Conformal time is defined as \eta = \int_0^{x_0} \frac{dx_0'}{a(x_0')}
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    Gauge transformations in GR

    Ok. I think have all papers ever written about this here, but all they say is that "one can easily see that..."
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    Gauge transformations in GR

    I don't follow. How does this couple with my metric transformation?
  26. L

    Gauge transformations in GR

    That I got, but how do I get your transformation?
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    Gauge transformations in GR

    I don't get it. Where does this come from?
  28. L

    Gauge transformations in GR

    If g_{\mu \nu} = \eta_{\mu \nu} + h_{\mu \nu} and g_{00} = -(1+2\psi) then h_{\bar{\mu} \bar{\nu}} = h_{\mu \nu} -\partial_{\mu} \xi_{\nu} -\partial_{\nu} \xi_{\mu} and h_{00} = -2\psi. But how do I get that \psi \rightarrow \psi + \alpha' + \frac{a'}{a}\alpha?? If I use the above...
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