Tuesday, January 26, 2010

Cations.

I have no interesting or fascinating idea or theory to tell you this morning. I also have no good questions.

Unless someone can help with:

Consider a uniformly charged ring in the xy plane, centered at the origin. The ring has radius a and positive charge q distributed evenly along its circumference. What is the magnitude of the electric field along the positive z axis?
E(z) =k\frac{qz}{\left(z^{2}+a^{2}\right)^{\frac{3}{2}}}

Imagine a small metal ball of mass m and negative charge -q_0. The ball is released from rest at the point (0, 0, d) and constrained to move along the z axis, with no damping. If 0 < d \ll a, what will be the ball's subsequent trajectory? = oscillating along the z axis between z = d and z = -d

The ball will oscillate along the z axis between z=d and z=-d in simple harmonic motion. What will be the angular frequency omega of these oscillations? Use the approximation d \ll a to simplify your calculation; that is, assume that d^2+a^2 \approx a^2. This is the one I'm having problems with. The closest I've gotten is:


w=


So yeah thats the meat and bones of my post this morning. More to come later maybe.

P.S. Cations are not part of the problem :p

1 comment:

fizziksman said...

Ah, I love that stuff. It makes me want to sit down and figure out the answer to your homework, just for fun.