Recent content by Inquisitive Student

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} =...

I would divide the total mass m by the total area A: $$\sigma = \frac{m_{tot}}{A}$$

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...

Yeah, NFuller had a very clear response. It was really helpful.

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...

Ok, but then how does one evaluate $$\vec{a} \cdot \nabla_v$$ in the vlasov equation? The acceleration vector is in spatial coordinates I believe.

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 =...