00:01
For this problem on the topic of inductance, we are told to assume that the magnitude of the magnetic field of a sphere of radius capital r at a distance little r away is given by the expression b0 into r, a big r over little r all squared, where b0 is a constant.
00:17
We want to use this and determine the total energy that is stored in the magnetic field outside the sphere and then evaluate the result for a given value of b0 and a given value of r, which are values.
00:30
That are appropriate for the earth's magnetic field.
00:34
Now, the total magnetic energy is the volume integral of the energy density.
00:41
The energy density little u is equal to the field strength squared, which is b squared over two times the magnetic constant u -0.
00:51
Because b changes with position, u is not constant.
00:55
And so for b is equal to b0 into r over r all squared, we get u to be b0 squared over to mu not multiplied by big r over little r all to the power 4.
01:17
Next we set up an expression for the magnetic energy that is stored in the spherical shell of radius little r and thickness d r...