# Magnetic Force Example

by Jared Rovny

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00:01 We have an example of a cyclotron problem here in which we ask what happens with an electric charge moving at a velocity of 1 meter per second through a field whose strength is 1 tesla, so this is a magnetic field.

00:13 The question is, what is the radius of the circle created by the motion of the electron if we're given that the mass-to-charge ratio of an electron is this very small number? So go ahead and use this cyclotron material that we've just discussed and see if you can solve for the radius of this path as the electron moves through a magnetic field.

00:33 Hopefully, what you did looks something like this.

00:35 What we have is again that we have a particle moving in some circle because it has a force towards the center of that circle.

00:44 This force is the force from the magnetic field and from our prior chapters we know that the force from the magnetic field, which we said is q times v times strength of the magnetic field has to be equal to mv squared over r, if it's gonna stay in this uniform circular motion.

01:03 But we're interested in, in this problem, is the radius of the path.

01:06 So let's solve for the radius rather than what we did earlier, the velocity.

01:10 You should get that the radius is equal to mv squared over q times v times B.

01:19 Do some quick simplifying cancelling one of these units of velocity.

01:22 We have mass times velocity over the charge times the magnetic field.

01:27 So how are we supposed to solve for this radius in terms of the givens? As what we know that we are given a velocity of 1.

01:34 Let's rewrite that 1 meter per second.

01:38 We know that we have a magnetic field of 1 tesla and we also know the mass-to-charge ratio of the electron.

01:46 So what is that? This is simply, this expression here, the mass-to-charge ratio, m over q.

01:52 Be aware that sometimes you're given the charge-to-mass ratio which will be a very, very different number so be careful to make sure you know what you're being given in the problem.

02:01 In this case, we have the mass-to-charge ratio.

02:04 We're told that this is, this a very small number, 5.7 times 10 to the minus 12 kilograms per coulomb.

02:14 And now we are ready to plug these values in by rearranging this equation here in terms of our knowns.

02:20 So we have m over q in this equation here on the left.

02:23 We also have a v over a B, so we'll have to plug those in as well.

02:29 So these are now our known quantities.

02:31 We now have the mass-to-charge ratio which is 5.7 times 10 to the minus 12th kilograms per coulomb times the velocity over the strength of the magnetic field, B, where the velocity is 1 and the strength of the magnetic field is also 1.

02:50 Since we've written everything here in terms of our simple SI units, our standard units, we don't have to worry about the units of the radius.

02:57 We know that they'll come out to be meters, so since these are just one the magnitude of this quantity stays exactly what it is 5.7 times 10 to the minus 12th and again we know all these units will boil down to our SI units since we used our standard units throughout the entire problem.

03:15 So this is a simple example of a cyclotron equation problem.

03:20 You can simply use the equations that we talked about for a cyclotron.

03:24 And again, always remember that the force of the magnetic field is going to work together with the equation we have for uniform circular motion in order to create the cyclotron equation which gets used very often.

03:36 This wraps up our discussion of the magnetic field and how it works.

03:41 Both its definition, how we talked about in measuring and defining it as well as the kinds of forces that charged particles experience when they are in the presence of a magnetic field.

03:51 Thanks for watching.

The lecture Magnetic Force Example by Jared Rovny is from the course Magnetism.

### Included Quiz Questions

1. 2.9 x 10 – 14 N
2. 4.9 x 10 – 13 N
3. 1.7 x 10 – 13 N
4. 3.4 x 10 – 14 N
5. 3.2 x 10 – 13 N
1. Deflect upwards
2. Deflect downwards
3. Deflect outside
4. Bounce back
5. Remains undeflected

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