Consider a one-dimensional situation on a straight line (say, $x$-axis). Let a charge of magnitude $q$ be located at $x=x_0$, the potential satisfies the Poisson's equation $$\frac{d^2V}{dx^2}=-\frac{\rho(x)}{\epsilon_0}=-\frac{q\delta(x-x_0)}{\epsilon_0}.$$ If $q>0$, $V^{\prime\prime}(x_0)<0$, and if $q<0$, $V^{\prime\prime}(x_0)>0$. Therefore, it appears that the potential $V$ does have a minimum at $x=x_0$, for $q<0$. Does this imply that $x=x_0$ is a point of stable equilibrium? I must be missing something because this appears to violate Earnshaw's theorem (or it doesn't)?
Subscribe to:
Post Comments (Atom)
Understanding Stagnation point in pitot fluid
What is stagnation point in fluid mechanics. At the open end of the pitot tube the velocity of the fluid becomes zero.But that should result...
-
I have an hydrogenic atom, knowing that its ground-state wavefunction has the standard form $$ \psi = A e^{-\beta r} $$ with $A = \frac{\bet...
-
I stand up and I look at two parallel railroad tracks. I find that converge away from me. Why? Can someone explain me why parallel lines s...
-
At room temperature, play-dough is solid(ish). But if you make a thin strip it cannot just stand up on it's own, so is it still solid? O...
-
This image from NASA illustrates drag coefficients for several shapes: It is generally accepted that some variation of the teardrop/airfoil...
-
Sorry if this question is a bit broad but I can't find any info on this by just searching. The equation q = neAL where L is the length o...
-
Sometimes I am born in silence, Other times, no. I am unseen, But I make my presence known. In time, I fade without a trace. I harm no one, ...
-
I want to know what happens to the space a black hole crosses over as our galaxy travels through space.
No comments:
Post a Comment