E=1/2mv^2 is equal to the total work done on the particle. You have two forces: the Lorentz force F=q(E+v*B) and gravitational force F=mg, both in the same direction (I assume j-hat is the unit vector in the y direction).
Hmm, so I write -∇(ΔΦ-(1/c^2)(∂^2Φ/∂t^2))=Δ(-∇Φ)-(1/c^2)(∂^2(-∇Φ)/∂t^2)=0. And this operation (i.e, taking nabla 'inside' the Laplacian and the partial time derivative) is allowed, right? There are no restrictions on it as far as I know but I'm not 100% sure.
Then I perform the same trick for...
I'm studying for my electrodynamics exam and one of the past exam questions is:
From the scalar and vector potentials, derive the homogenous wave equations for E and B fields in vacuum.
I did derive the wave equation for the B field by simply taking the curl of the homogenous wave equation for...
So you suggest I use Vo = 1 J? If I do that, I will get
bα = b*√[2m(Vo − E)]/(h/2π) = 3√(2*1000*(1-1/2)/(1.054*10^-34)) ≈ 10^36. With Vo = 1 J, E = 0.5 J the equation (i) becomes
T=1/(sinh(bα))^2.
New problems arise:
1) WolframAlpha didn't calculate (sinh(10^36))^-2 so I did a Taylor...
Homework Statement
A car (particle) with mass m = 1 t drives into a barrier with a height of 1 m and a thickness of 3 m. The kinetic energy shall be sufficient to get classically over a barrier with half of the height. Derive an equation for the tunnelling probability. What is the probability...