An electron experiences a magnetic force of magnitude 4.60x10^-15 N when moving at an angle of 60.0° with respect to a magnetic field of magnitude 3.50x10^-3 T. Find the speed of the electron.

Video transcript

Hey, everyone, this problem is working with magnetic fields. Let's see what they are giving us and what they're asking from us. So we have a proton, it's projected into a uniform magnetic field of a given magnitude. It is subjected to a magnetic force Of another given magnitude. And the angle between the protons velocity and the direction of magnetic field is also given to us as 45°. What is the protons speed? So that's what we're looking for here in this problem, the speed. So the first thing we can do is recall that the force from a magnetic field is given by the equation F equals the absolute value of Q V B times sine of data. So let's take each of those terms, one by one Q is our charge. We know that we have a proton. So we can recall that the charge of proton is 1.6 times 10 to the negative columns, it's positive. So the absolute value is going to the same positive 1.6 times to the minus 19 Coghlan's V is the velocity or speed. And so that's what we're solving for B is the magnitude of the magnetic field that's given to us in the problem at 4.2 times 10 to the - Tesla. And that our angle data is also given to us. The problem um is the angle between the velocity and the direction of the magnetic field which is 45° spread out a little bit better there, 45 degrees and force F is given to us in the problem, magnetic force magnitude of five Times 10 to the -15. So if we rearrange this equation to solve for V, we actually have everything we need to just plug and chug. So I'm going to rewrite that as B equals F over Q absolute value of Q B times the sine of data. When we plug in our values here, We have five times 10 to the -15 newtons over 1.6 times 10 to the - columns. For our charge, Our magnetic field magnitude is 4.20 times 10 to the -3 Tesla and our angle is 45. So sign of 45 plug that into our calculators and we get 1.5 times 10 to the seven meters per second. So that's the answer to our problem. When we look at the potential choices that aligns with answer C. So C is the correct choice for this problem. That's all we have for this one. We'll see you in the next video