I just had a pretty neat problem on my Electrodynamics (course text) mid-term. The problem is to solve for the electric field for two charged conducting spheres of different radii connected by a conducting filament so they reach the same potential.
The result (pdf of full solution) is that the electric field is greater near the surface of the smaller sphere even though it carries less of the total charge. The physical implications of this is that the electric field will be high near the parts of a charged conductor that have a small radius of curvature (ie corners). That's why you get arcing and sparking on forks and crumpled aluminum foil that you put in the microwave.
Showing posts with label electrodynamics. Show all posts
Showing posts with label electrodynamics. Show all posts
Sunday, November 16, 2008
Saturday, November 8, 2008
EM Flash Cards
I just discovered a great new plug-in (in time for mid-terms) for OpenOffice.org Impress called Open Cards. It is uses the titles of the slides as the question and the body of the slide as the answer to the flashcards. It keeps track of your learning state, has a couple of different learning modes, and seems to use some pretty sophisticated training algorithms.
I put together a set of flashcards for electrodynamics if you're interested in trying it out (of course you need Open Office installed to use the file).
I put together a set of flashcards for electrodynamics if you're interested in trying it out (of course you need Open Office installed to use the file).
Wednesday, October 22, 2008
Current in the middle of the Earth
What if the Earth's magnetic field were caused by a current loop in the mantle?
This can be a decent approximation because the Earth's magnetic field is roughly that of a dipole.
It's easy to look-up the Radius of the earth, and we can use a rough estimate of 0.23 gauss for the horizontal component of the magnetic field at 40 degrees latitude.
A simple expression for the magnetic field due to a dipole in spherical polar coordinates is
There's no dependence on azimuthal angle because of the symmetry axis along the dipole.
The dipole moment is then
And the current in a loop 1/3 the radius of the earth required to create a field of that strength is
That's a lot of statcoulombs!
This is Problem 2.2 from Classical Electromagnetic Radiation
; Chapter 2 covers multi-pole expansions of static electric and magnetic fields.
This can be a decent approximation because the Earth's magnetic field is roughly that of a dipole.
It's easy to look-up the Radius of the earth, and we can use a rough estimate of 0.23 gauss for the horizontal component of the magnetic field at 40 degrees latitude.
A simple expression for the magnetic field due to a dipole in spherical polar coordinates is
There's no dependence on azimuthal angle because of the symmetry axis along the dipole.
The dipole moment is then
And the current in a loop 1/3 the radius of the earth required to create a field of that strength is
That's a lot of statcoulombs!
This is Problem 2.2 from Classical Electromagnetic Radiation
; Chapter 2 covers multi-pole expansions of static electric and magnetic fields.
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