Recent content by ptr

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    Net force between two identical dipoles

    You can find the fields, and use superposition on the fields, and then multiply by the charge. The field of a dipole and also that of the other charge, that is.
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    F''(x) Second Derivative problem

    Try taking the first derivative first, then take the second derivative.
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    Matrix exponential

    The actual sum would depend on element of the domain chosen where the image is to be evaluated.
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    Funny question

    The time allowed for acclerating is longer if the pad is hit than if something with a high elasticity is hit, then the force would be less because force is change in momentum relative to change in time. Are you all right?
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    Series question

    Exponents of the form n^n grows much faster than factorials of the form (n!) because the factorial is a multiplication of n terms, the majority of which are less than n, and the power is a multiplication of n terms, all of which are equal to n.
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    Matrix exponential

    Yes, sorry, I meant, in a series, not closed form, hahah, do you need the actual sum?
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    Need help setting up triple integral in spherical coordinates

    The boundaries are given by the limits to the integration. How did you arrive at the limits? No, they are not wrong, if the center of the sphere is at the point where all the cartesian coordinates are zero.
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    Divergence Problem

    Integrate over the surface using the transformation to cylindrical co-ordinates, using x = square_root(16) cos(theta) and similarly for y, and the divergence theorem gives support to your integrating over the vector field, once you have added in the jacobian, from zero to two pi for theta, and...
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    Matrix exponential

    Notice \begin{bmatrix}-1 & 2 & 0\\-2 & -1 & 0\\ 0 & 0 & -3\end{bmatrix} ^i = \begin{bmatrix}{((-1)^i (2i-1))} & {((-1)^{i-1} 2i)} & 0\\{(-1)^{i} 2i)} & {((-1)^i (2i-1))} & 0\\ 0 & 0 & (-3)^i\end{bmatrix}. The series then is easily represented in a closed form.
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    Voltage and current calculation on a mixed circuit

    It might be well to read up on "Delta-Wye" transformations.
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    Different dielectric material with different relative permittivity

    The voltage between the plates remains, unchanging, the capcitance is calculated by, C_{ca} = {\epsilon}_0 {\epsilon}_r \frac {A}{d}. This in fact happens in real life, when capacitors are heated and one of the two plates in a parallel plate capacitor pulls away from the dielectric, another...
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    Simple Temperature problem

    Try using the other equation you have, though I know not what it is, and then, \Delta V = (1-\frac{1}{8}) V_0, from which it seems that the original volume is not here required. -the final temperature is the change in temperature plus the original temperature
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    Very very quick quiestion about D_4?

    Forgive me, I am probably wrong, but I thought that the mapping from 1234 to the permutations that go along with the reflections and rotations described were the automorphisms, and the automorphisms formed the automorphism group of the dihedral group that we are talking about. In which case, the...
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    Underwater Lightbulb Optical Illusion - Reflection/Refraction of Light

    The refraction of light from water to a curved glass then to air might cause the glass of the light bulb to look thicker. An optically opaque coating has no index of refraction of meaning, and is not part of the explanation.
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    Very very quick quiestion about D_4?

    Consider a square, and label the vertices 1, and 2, and 3, and 4. Then, proceed to record the automorphisms as you rotate it and reflect it along its axes of symmetry. Then, you'll be able to find all eight automorphisms if you do not forget, as some might, though I trust you wouldn't, the...
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