The speed of light in vacuum is 1 / sqrt(mu_0 e_0). In matter, this is modified using relative permittivity and permeability, so the speed of light in matter is c / sqrt(k_m k_e).
In diamagnetic materials, isn't k_m < 1? Then we'd have light going faster than 3 * 10^8 m/s in, say, nitrogen...
Would this have anything to do with special relativity? I remember seeing something about length contraction when switching reference frames once, and about how that produced a charge density out of nowhere.
Edit: what if there's a nonzero resistance?
Homework Statement
One step in one of the problems in my book (involving calculation of the Poynting vector) asks to find the electric field outside a wire. This wire is resistanceless and the current is steady.
Homework Equations
Maxwell's.
The Attempt at a Solution
Stared at...
Your initial observation was good; using this equation is overkill. But, using it:
The block starts at the farthest point, so the phase constant is zero. So
x(t) = A cos(ωt)
Now, if you wanted to find the position at time t = 0, you'd have
x(0) = A cos(ω0) = A cos(0)
They told you...
Two tricky MC problems from Halliday/Resnick:
1. A point charge is placed inside an uncharged spherical conducting shell, somewhat off center. However, the charge distribution on the outer surface of the shell is uniform. Why?
2. What is the minimum number of resistors necessary to make a...
The first one is correct in general (i mean, unless the spring itself has mass, but that would be ridiculous!). It's just Hooke's Law.
The second one is more complex. Imagine quickly hooking on the weight: the weight is going to start oscillating on the spring, with the center of oscillation...
If a is the acceleration of an electron in a conductor due to an electric field, and t is the mean time between collisions, than v_d, the average drift velocity, is
v_d = at
1. There should be a 1/2 there! If you followed one electron, its average v_d would be at/2 by kinematics.
2. Book...
Say you have two spherical conductors, of radius r, centers a distance d apart. Both have charges of +Q. What are the charge distributions on them?
My physics book more or less handwaves and says it'll be more or less unaffected, but is there a way to solve this exactly?
Alright, that makes sense. Is this reasoning right?
The potential of the can is raised, since negative charge moves to the inside to balance out the sphere's charge and positive charge moves to the outside. The can was at V = 0 previously because it was uncharged, but now V > 0.
The...
What do they mean when they refer to it? The PE of a system, I get, and the potential of a point is the work per unit charge needed to bring a charge there, assuming the charge has no effect on the field (right?).
A small conducting sphere originally has a charge +q. The sphere is lowered...
My physics book explains a van de Graaff in this way:
A small conducting sphere of radius a and carrying charge q is located inside a larger shell of radius b that carries charge Q. A conducting path is momentarily established between the two conductors, and the charge q then moves entirely to...
I want a MV Calc book that has a good covering of vector field operations, mostly for studying Maxwell's equations and stuff later on. Rigor would be nice; I would prefer a book that proves most theorems, but not one as crazy as Spivak (I have only a few months!). Interesting theoretical...
Homework Statement
Find parametric equations for the hypocycloid that is produced when we track a point on a circle of radius 1/4 that rotates inside a circle of radius 1. Show that these equations are equivalent to (sin^3 t, cos^3 t).
Homework Equations
N/A
The Attempt at a Solution
I...