I got this:
y = \pm x
(x^2+x^2-4)(x+x)=0
x(x^2-2)=0
x = 0 \vee x=\pm \sqrt{2}
According to the solutions manual, which only states the values, not the method, the solutions are:
x = \pm \sqrt{2} \vee x = \pm \sqrt{\frac{2}{3}}
So, if you want to calculate the gravitational force a massive object of mass M exercises on some other mass m, it would be done like this:
F_G = -G\frac{mM}{r^2}. Where F_G is the gravitational force, G the gravitational constant and r the distance between the two objects. (either as size or...
Thanks for your advice.
However, this doesn't give me the four points of intersection. If I take the solutions y=\pm x, I get the solutions (0,0) \wedge (\pm \sqrt{2},\pm \sqrt{2}).
However, the points (\pm \sqrt{\frac{2}{3}},\pm \sqrt{\frac{2}{3}}) are also solutions of the equation. And...
This is because you are dealing with electrostatics. If the charge is moving rapidly, you are dealing with electrodynamics and magnetic fields. I don't really know what exactly is slow enough to be described by electrostatic theorems, though.
Hi,
I am studying for my Analysis final and came across this problem I just can't get my head around:
Homework Statement
Find the critical points of f(x,y) = (x^2+y^2-4)(x+y) and their nature.
Homework Equations
\vec{\nabla} f(x,y) = \vec{0}
The Attempt at a Solution
\frac{\partial...
Thanks for your answer!
So, I tried to draw the contributions. Am I correct that inside the circle the dE due to the negative charge points toward the negative charge and dE due to the positive charge also points in that direction, thus doubling the field? Or is this too naive?
For a point...
Well, the plane is defined as \vec{r} \cdot \vec{n} = 0. This states that r is perpendicular to n. So every point r for which this equation holds, lies in the plane. See also this page on planes: http://mathworld.wolfram.com/Plane.html. Hope this helps!
Homework Statement
Given a circular wire with radius R. Choose the origin in the center of the circle, the z-axis perpendicular to the circle. One halve of the circle contains a positive line charge \lambda, the other halve a negative line charge of the same magnitude.
(a) Sketch the electric...