Physics Help!!!?

Question

Protons having a kinetic energy of 5.50 MeV are moving in the positive x-direction and enter a magnetic field of 0.0520 T in the z-direction, out of the plane of the page, and extending from x = 0 to x = 1.00 m
Calculate the y-component of the protons' momentum as they leave the magnetic field in kg*m/s

Answer 1

Tennis, this one is a good one. You have to use what you are currently learning about magnetic fields with topics you learned probably four to six months ago about momentum, work, energy and force.

We need to have a few constants which will make this easier:

The charge of a proton: q = 1.60 x 10^-19 C
The mass of a proton: m = 1.673 x 10^-27 kg
1 eV = 1.60 x 10^-19 J

First we must know how fast the protons are moving:

T = 1/2 m v^2 where T is kinetic energy in joules

5.50 MeV * 1 x 10^6 eV / 1MeV *1.60 x 10^-19 J/ 1 eV = 8.8 x 10^-13 J = T

v = (2 T / m)^2 = 3.24 x 10^7 m/s

Now we know how fast the protons are moving we can find the force acting upon the protons within the magnetic field. Use the right hand rule to determine the direction of this force.

F = q v B

F = 1.6 x 10^-19 C * 3.24 x 10^7 m/s * 0.052 T = 2.70 x 10^-13 N

There are a number of ways you can proceed from here. The way I will proceed is modeling this as a projectile motion problem. This force does work on my proton which will increase it's velocity. The tricky part is this force is not in the direction of motion or opposite the direction of motion. You could also model this as a work-energy problem as well.

I will need to know how long it is in the magnetic field and what acceleration it feels in the magnetic field.

d = v t, where d is the horizontal (x-direction) distance in the field

t = d / v = 1.00 m / 3.24 x 10^7 m/s = 3.1 x 10^-8 sec.

I will also want to know what acceleration it feels

F = m a

a = F / m = 2.70 x 10^-13 N / 1.673 x 10^-27 kg = 1.61 x 10^14 m/s^2

I can now find the final velocity of the proton in the y-direction using the equation:

v = v0 + a t = a t = 1.61 x 10^14 m/s^2 * 3.1 x 10^-8 sec =5.00 x 10^6 m/s

We have now found the y-component of velocity. Now we must find the y-component of momentum:

p = m v = 1.673 x 10^-27 kg * 5.00 x 10^6 m/s = 8.37 x 10^-21 kg m/s

You must also find out if this is in the + or - y-direction, use the right hand rule to find this.

Good luck.