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  1. X

    Strength of magnetic field required to balance gravitational force

    Begin by looking at the equations for force due to a magnetic field and force due to gravity.
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    Mass places o that it is in equilibrium

    So that what is in equilibrium? I believe you are missing part of the question.
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    Magnetic Field of A Toroid

    I believe that is a mistake in the text. I think he meant it to be the vector r and not r hat, in which case the denominator would be cubed.
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    Circular Motion

    Okay. So, what would happen if the centripetal force became greater than the weight?
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    Circular Motion

    Do you mean maximum? The minimum speed would be zero.
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    Capacitor with dielectric

    This should be D = ε0εrE Where are those 2's coming from?
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    Finding net force, acceleration and speed.

    What forces are acting on the motorcycle? In what directions are these forces acting?
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    Tension and Pulleys Cannot understand this problem

    Draw a free body diagram. How many tension forces T are there? What direction are these tensions in? Is it possible for them to "cancel" each other out?
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    Inductance problem

    I get I = 0.707 A.
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    Inductance problem

    You don't want to use V=IR, that doesn't take into account the reactance of your inductor. For a simple LR circuit V=IZ.
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    Spring motion

    Do not set the first two equations equal to each other, they are not equal. The two forces acting on the mass, the weight and spring force, add to give the total force which will be zero when x=d.
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    Help with Torque Problem

    The moment is a cross product, you haven't taken into account the angle between the moment arm and the force.
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    What is the angular speed in revolution per minute?

    It seems like you are taking the correct steps. However, I get a different numerical answer than you do. Also, may I suggest that you don't plug all of those numbers in immediately, and just work with symbols until you have an expression for what it is you are looking for? It'll make the...
  14. X

    Related Rates (increasing cone radius question)

    A variable to the first power's derivative is equal to one only when differentiating with respect to that variable. So, dh/dh=1, but dh/dt doesn't necessarily. You don't have to, but you would need to find dh/dt in terms of r and dr/dt and substitute that at some point. Personally I think it...
  15. X

    Finding the bound charge in a dielectric ATTEMPT 2

    And I realized my mistake with the negative sign on \sigma_b, I was thinking of the surface of the plate rather than the surface of the dielectric.
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    Finding the bound charge in a dielectric ATTEMPT 2

    And I meant one half Q_f for both cases.
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    Finding the bound charge in a dielectric ATTEMPT 2

    Sorry, that was a typo. Only the volume bound charge was meant to be negative.
  18. X

    Finding the bound charge in a dielectric ATTEMPT 2

    Great, I am getting that Q_b=0 now, with the bound volume charge equal to negative one half and the bound surface charge to be negative one half. Thank you so much.
  19. X

    Finding the bound charge in a dielectric ATTEMPT 2

    I get negative because \hat{n}=-\hat{i} since x is increasing as you move from the first plate (x=0) to the second (x=d). I just re-did my calculation for \rho_b and I got d in the numerator now, and the whole thing has a negative sign. This will change my \int \rho_b dx and hopefully give...
  20. X

    Finding the bound charge in a dielectric ATTEMPT 2

    Homework Statement The space between the plates of a parallel plate capacitor is filled with a dielectric material whose dielectric constant ϵr varies linearly from 1 at the bottom plate (x=0) to 2 at the top plate (x=d). The capacitor is connected to a battery of voltage V. Find all the bound...
  21. X

    Finding the bound charge in a dielectric

    ehild, I was looking at this problem again, and your suggestion. I don't understand how finding the voltage the way you describe helps me find bound charge. Could you please elaborate?
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    Finding the bound charge in a dielectric

    Yeah, I realized right after I posted, sorry. I feel like an idiot, I wasted a lot of time attempting the wrong problem.
  23. X

    Finding the bound charge in a dielectric

    I am sorry. I was misreading the question. I was thinking "bottom OF THE plate" and "top OF THE plate." Your interpretation of it is correct, it is the "bottom plate" and "top plate." Thanks. This may have been where all my confusion came from. I'll have to start fresh on it.
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    Finding the bound charge in a dielectric

    No, you are misreading the question. The ε is constant in the plane perpendicular to the plates. The x-axis is running along the plate.
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    Finding the bound charge in a dielectric

    ehild I was actually thinking of slicing perpendicularly to the plates, so that the dielectric in each slice had the same ε_{r}, and that way the slice capacitors would be connected in parallel.
  26. X

    Finding the bound charge in a dielectric

    How do I delete a post? I thought latex worked here and I think it would be easier just to start this over?
  27. X

    Finding the bound charge in a dielectric

    MODERATOR'S NOTE: problem statement is mistaken, please see https://www.physicsforums.com/showthread.php?t=723342 Homework Statement The space between the plates of a parallel plate capacitor is filled with a dielectric material whose dielectric constant $\epsilon_r$ varies linearly from 1 at...
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