No problem about the vector notation.
The reason I wondered if there was more to the question because, in general, dv/dt wouldn't be zero.
Look up "velocity selector", for example https://en.wikipedia.org/wiki/Wien_filter (must admit I learned something as well, I never realised that velocity...
I think you first have to realise that you are dealing with vector quantities.
With just a magnetic field of strength B you have the force acting on a charge q moving with velocity v is mdv/dt = q vXB (where vectors are bold face).
In this situation if you assume that the charge moves...
I think you have made a mistake in some of your +ve/-ve signs and think that your approach would eventually give y = y.
The best way to go about this is to write cosx =(exp(ix) + exp(-ix))/2 (Euler's formula) and then you have to solve a differential equation of the form
dy/dx = exp(mx) where...
This is a request about the second order differential equation
y'' + (k^2 + f(r))y(r) = 0 (1)
where k is a (real) constant and f(r) is a real valued function of r that has some constraints regarding integratability.
The terms met with in electricity have some historical bias. Voltage appears to come from the name of the scientist Alessandro Giuseppe Antonio Anastasio Volta who was one of the first people to investigate electric circuits (http://en.wikipedia.org/wiki/Alessandro_Volta)
One way to introduce...
Mass isn't invariant: It is the total mass+energy that is conserved.
As well, I'm not sure if you're aware of the well known formula from special relativity that relates the mass of a particle to its speed v: m = m0/sqrt( 1 - v^2/c^2)?
You may consider using the following:
gradXA = B
then use Stoke's theorem to write surface int(gradXA.dS) = line int (A.dl), with the closed curve chosen suitably.
This gives line int(A.dl) = int(B.ds).
The surface integral is straight forward...
You dont have a wave equation there, you have solutions to a wave equation.
As well, since cos(-z) = cos(z), i.e. cos is an even function you can write the cos solution as A cos (ωt - kx) if you wish.
The general solution to the wave equation is
Acos(wt - kx) + Bsin(wt -kx)
where A and B...