00:01
For this question, we're going to consider an electron moving at a speed v of 1 times 10 to the 4 meters per second in a circular path of a radius r of 0 .2 centimeters inside the solenoid.
00:11
So i convert centimeters to meters, so this is 0 .02 meters is 0 .02 meters.
00:17
We're asked to find the magnetic field inside the solenoid for part a.
00:21
So to do this, we're going to consider the fact that the force from the magnetic field, f sub m, is equal to the centripetal force f sub c, if there's a no acceleration for the electron and there's only a constant velocity.
00:34
So the magnetic force is equal to the charge of an electron, which is e, times the velocity of the electron v times the magnetic field it's experiencing b.
00:44
This is equal to the mass of the electron m times the velocity squared divided by the radius of orbit r.
00:51
So we can rearrange this to solve for b.
00:54
We find that b here is equal to mv, since one of the vs cancel here, so that's a square cancels with that v term since they're the same.
01:04
So this is mv over the charge of the electron e times r.
01:09
So we know v and r.
01:10
We were given those in the beginning.
01:12
M here is just a constant.
01:13
It's the mass of the electron, and we want that in kilograms...