Helical Trajectory - magnetic field

[GDGirl]

Homework Statement

An electron enters a uniform magnetic field B = 0.246 T with its velocity vector making an angle of θ = 49.7 ° with respect to the B vector. Determine the radius r and the pitch p (distance between loops) of the electron's helical path assuming its speed is 3.0 x 106 m/s.
HELP: In considering the circular part of the motion, you can ignore the component of the velocity vector vx along the direction of the magnetic field. (If you like, think of the electron's trajectory as seen by an observer moving along the B direction with speed vx. For that observer, the electron is moving in a circular orbit, rather than a helix.)
HELP: Figure out how long the electron takes to complete one loop of its orbit. How far along the B direction does the electron drift during this time?

Homework Equations

r=mv/qB
I'm not sure of any others.

The Attempt at a Solution

I'm still at the finding r stage. So as per the "help" I used said equation, and got 6.943x10^-5 as the answer. However, it's not correct. I'm not quite sure what I'm doing wrong.

 

[Doc Al]

I'm still at the finding r stage. So as per the "help" I used said equation, and got 6.943x10^-5 as the answer. However, it's not correct. I'm not quite sure what I'm doing wrong.

Show exactly what you did and the values you used. For example, what did you use for v?

 

[GDGirl]

I used 3.0x10⁶ m/s for velocity. It says speed, but I know velocity's units are m/s so I figured it was right... Was I wrong?

 

[Doc Al]

I used 3.0x10⁶ m/s for velocity. It says speed, but I know velocity's units are m/s so I figured it was right... Was I wrong?

Yes, that's incorrect. That equation (r = mv/qB) assumes a circular orbit with v perpendicular to B. Per the first hint, you need to use the component of the velocity perpendicular to the B field.

 

[GDGirl]

Yes, that's incorrect. That equation (r = mv/qB) assumes a circular orbit with v perpendicular to B. Per the first hint, you need to use the component of the velocity perpendicular to the B field.

I'm afraid I don't quite understand the difference then... I figured that what I was doing wrong had something to do with the angle, but I don't know what the difference is.

 

[Doc Al]

Start by finding the components of the velocity parallel and perpendicular to the magnetic field. You have the angle. The given speed is the total velocity; to use in that equation, you need the component perpendicular to the B field.

 

[GDGirl]

That makes perfect sense now, thank you so much!

 

[GDGirl]

okay, so now I'm having problems with the second part. I found the time that it takes for it to complete one orbit using T=2(pi)r/v
So: T=2(pi)(5.295x10^-5/(3.0x10⁶
which gave me 1.109x10^-10 seconds.
I multiply this by the velocity, which means that I can basically just using 2(pi)r for the formula, which is just the circumference. Anyways, this gave me 3.327x10^-4. This is wrong and I don't know why. I even checked in the book (we do book problems with randomized numbers) and when I solved the problem in the book using the same method, I get it correct according to the back of the book.

 

[Doc Al]

I found the time that it takes for it to complete one orbit using T=2(pi)r/v
So: T=2(pi)(5.295x10^-5/(3.0x10⁶
which gave me 1.109x10^-10 seconds.

Careful: Since here you are seeking the period of the circular orbit, which component of velocity should you be using?

I multiply this by the velocity, which means that I can basically just using 2(pi)r for the formula, which is just the circumference.

Careful: Since you are finding the distance along the B direction, which component of velocity should you be using?

 

[GDGirl]

Aha, that makes sense. Thanks again!