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?
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.
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...
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...
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.
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...
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...
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?
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.
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.
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...