Determine the magnitude of the field?

Question

In a linear accelerator, protons are accelerated from rest through a potential difference to a speed of approximately 2.69x10^6 m/s. The resulting proton bean produces a current of 1.03x10^-6 A. The mass of the proton is 1.67x10^-27 kg. and its charge on the proton is 1.6x10^-19 C. The proton beam enters a region of uniform magnetic field B, as shown below, that causes the beam to follow a semicircular path. Determine the magnitude of the field that is required to cause an arc of radius 0.104 m. ANswer in units of T.

Answer 1

First of all you will have to remember that:
Radius = mass x velocity / charge x field
This can be deduced by equalying the centripetal force to the magnectic force. You will propably find this in you book.

Using the first formula.

0,104 m = 1.67x10^-27 kg x 2.69x10^6 m/s / 1.6x10^-19 C x field

0,104 m = 4,4923 x 10^-21 / 1,6 x 10^-19 x field

1,6 x 10^-19 x field x 104 x 10^-3 = 4,4923 x 10^-21

16,64 x 10^-21 x field = 4,4923 x 10^-21

field = 4,4923 \ 16,64 =~ 0,269 T

I hope I helped you!

Answer 2

Wowser's - I'm just doing your A-Level homework.....

q v B = m v^2 / R

Therefore-: B = m v / q R

B = 1.67 x 10^-27 x 2.69 x 10^6 / 1.6 x 10^-19 x 0.104

B = 0.2699699519 Tesla

Could easily supply that magnetic field with a permanent ferrite magnet !!!!