Principles of Plasma physics by Krall & Trivelpiece seems to be a well-used book in the plasma physics community, but I've never seen a solution key for the questions asked in the book. I am trying some of the problems and want to check my work.
Is there such a solution key or some blog that...
In the uniform density case you had $$\lambda = \frac{m}{L}$$ where in this case L is the distance in x. Then you divide by the y coordinate to get the area density.
So then it looks like it should be l = y (or maybe l = dy because you have $$\iint (\lambda(x) / l) dxdy = \int \lambda(x) dx$$)
Is this what you mean:
$$\sigma = \frac{m_{tot}}{L^2}$$
but the total mass is equal to the masses of the infinitely thin lines that you stack up together to create a square:
$$\frac{\int_0^L {\lambda(x) dx} * L}{L^2} = \frac{\int_0^L {a*x dx} * L}{L^2} = \frac{a *\frac{L^2}{2}* L}{L^2} =...
Given a square with a linear mass density of:
λ(x) = a * x (see image below where black is high density and white is low density)
how would you deduce what the surface mass density is?
I get confused for the following reason:
To me it seems that the surface mass density should depend on x...
From boundary conditions we know that Φ(x = 0) = 0 (stated in the problem that left wall of parallel plate capacitor is at Φ = 0) and that Φ(x = L) = V. Poisson's equation in space (we neglect the charge in the problem, we are just finding the potential due to the walls) is ∇2Φ = 0, or in 1D...
Homework Statement
Find the total amount of energy of a charge (q) initially at rest placed at the left plate of a parallel plate capacitor. The left plate is at V = 0, the right plate at V = V0 and the plates are a distance L apart.
Homework Equations
Etot = 1/2 mv2 + qφ(x).
φ(x) = Vx/L
The...
Homework Statement
The vlasov equation is (from !Introduction to Plasma Physics and Controlled Fusion! by Francis Chen):
$$\frac{d}{dt}f + \vec{v} \cdot \nabla f + \vec{a} \cdot \nabla_v f = 0$$
Where $$\nabla_v$$ is the del operator in velocity space. I've read that $$\nabla_v =...