An electron moves in a circle of radius R in a uniform m a...

An electron moves in a circle of radius $R$ in a uniform $m a g-$ netic field $\overrightarrow{\mathbf{B}}$. The field is into the page. (a) Does the electron move clockwise or counterclockwise? (b) How much time does the electron take to make one complete revolution? Derive an expression for the time, starting with the magnetic force on the electron. Your answer may include $R, B$, and any fundamental constants.

Transcript

00:01 Okay, an electron is moving in a circle of radius r and a magnetic field b.

00:06 The field is into the page.

00:10 So we'll draw this real quick.

00:23 Does the electron move clockwise or counterclockwise? so let's just imagine we somehow get the electron in here.

00:34 I mean, we could shoot it in from the left or whatever.

00:38 But we get it in here and it's moving to the right.

00:42 So let's think about what the force, magnetic force is going to do.

00:48 So the magnetic force is equal to q times v crossed with the b.

00:57 So for an electron, you can use the right -hand rule and then do the opposite of what you get, or you can use the left -hand rule since it's a negative charge.

01:06 So qv -cross -b, the force is going to deflect the electron down.

01:13 Okay, so now let's just pretend here's our electron.

01:17 It's moved down a little bit.

01:19 So now we do qv cross b.

01:21 The force is pushing it this way.

01:24 So we can keep doing this and see that our electron is going to move kind of like this.

01:34 If you do it enough times, you can see that it's forming a circle of radius r and that the motion is clockwise.

01:56 So i guess that's part a.

02:01 Clockwise is the answer.

02:05 Okay, so now we want to find the derivation, or how much time does it take to make one complete revolution, derive an expression starting with the magnetic force, so we can use r, b, and fundamental constants, probably like the mass or the charge...

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