A proton moves through a uniform magnetic field given by...

A proton moves through a uniform magnetic field given by $\vec{B}=(10 \hat{\mathrm{i}}-20 \hat{\mathrm{j}}+30 \hat{\mathrm{k}}) \mathrm{mT}$. At time $t_{1}$, the proton has a velocity given by $\vec{v}=v_{x} \hat{i}+v_{y} \hat{j}+(2.0 \mathrm{~km} / \mathrm{s}) \hat{\mathrm{k}}$ and the magnetic force on the proton is $\vec{F}_{B}=\left(4.0 \times 10^{-17} \mathrm{~N}\right) \hat{\mathrm{i}}+\left(2.0 \times 10^{-17} \mathrm{~N}\right) \hat{\mathrm{j}} .$ At that instant, what are (a) $v_{x}$ and (b) $v_{y}$ ?

Transcript

00:01 Okay, we have a proton moving through a uniform magnetic field, and we're given the velocity and the magnetic field and the force that it feels.

00:12 And we want to find what are vx and vy.

00:19 So let's just write this out.

00:20 B equals 10, i -hat minus 20, j -hat, plus 30 k -hat, milat -tesla.

00:35 We're going to write times 10 to the minus third tesla.

00:40 Okay, v equals vx, i -hat, plus vy, j -hat, plus, and i'm just gonna convert this right now, 2 ,000 k -hat meters per second.

01:04 Okay, and the force is 4 times 10 to the minus 17, i hat plus 2 times 10 to the minus 17 j hat and then plus 0 k hat newtons right so when we're doing these calculations it's important to make sure you have everything in tesla meters per second and newtons so i put the 10 to the minus third on the outside here but when you you for example plug in bx or b y right so 10 or negative 20 make sure you also include the times 10 to the minus third or you'll get you'll get the wrong answer right so that's important to note is to have the right units okay so the equation we're going off right is force equals q v cross b what's q well it's a proton so it has an elementary charge 1 .6 2 times 10 to the minus 19 coulums.

02:17 So it's the charge of an electron, but just positive.

02:23 So let's just write down what this cross product looks like.

02:32 So if we were to, you can perform the cross product, you know, using a computer or using the matrix determinant method, i'm just going to kind of write down what the cross product looks like if you just look at each, like if you just want a formula to just kind of follow, right? so let's write this down.

03:02 So the x component of force will be given by, and this is all going to be multiplied by q...

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