Recent content by mXCSNT

Revised guess for center P: P = \alpha + Rn - (R')Tb so now the constant radius follows immediately and I simply have to show that P itself is constant.

So if I assume that the "const" in question is the square of the radius, that could make R and (R')T the lengths of respective legs of a right triangle whose hypotenuse is the radius. I know that R is the radius of curvature, so drawing a diagram I'm guessing that the center P is P = Rn -...

My mistake, I misread it... first map the real line to the interval (0, 1) then count all the intervals whose image under that map have length at least 1/2, of which there are at most 1.

You could start by counting all the intervals of length at least 1/2.

Homework Statement Assume that \tau(s) \neq 0 and k'(x) \neq 0 for all s \in I. Show that a necessary and sufficient condition for \alpha(I) to lie on a sphere is that R^2 + (R')^2T^2 = const where R = 1/k, T = 1/\tau, and R' = \frac{dr}{ds}Homework Equations \alpha(s) is a curve in R3...

We also have Gauss' law \oint_S \vec{E} \cdot d\vec{A} = \mu_0 Q_{enclosed}, and I remember the professor saying something about considering the situation as the slab is gradually moved in from one side a distance x, but I don't have any ideas. I still don't see what causes any force on the...

Homework Statement An air-insulated parallel-plate capacitor of capacitance C_0 is charged to voltage V_0 and then disconnected from the charging battery. A slab of material with dielectric constant \kappa, whose thickness is essentially equal to the capacitor spacing, is then inserted...