Question

An antiproton is identical to a proton except it has the opposite charge, −e. To study antiprotons, they must be confined in an ultrahigh vacuum because they will annihilate−producing gamma rays−if they come into contact with the protons of ordinary matter. One way of confining antiprotons is to keep them in a magnetic field. Suppose that antiprotons are created with a speed of 4.0 × 104 m/s and then trapped in a 4.0 mT magnetic field.

Answer 1

Answer:

d = 1.13*10^{-4}m = 0.113mm

Explanation:

To find the minimum diameter, that allow to antiproton circulate in the chamber without touching the walls, you use the following formula for the radius of the trajectory of a charged particle in a constant magnetic field.

$r=\frac{mv}{qB}$   (1)

r: radius of the trajectory

m: mass of the antiproton = 9.1*10-31 kg

v: velocity of the antiproton = 4.0*10^4 m/s

B: magnitude of the magnetic field = 4.0mT = 4.0*10^-3 T

q: charge of the antiproton = +1.6*10^{-19}C

You replace the values of the parameters in (1):

$r=\frac{(9.1*10^{-31}kg)(4.0*10^4m/s)}{(1.6*10^{-19}C)(4.0*10^{-3}T)}\\\\r=5.68*10^{-5}m$

Then, the diameter of the chamber must be, at least:

d=2r = 2(5.68*10^-5) = 1.13*10^{-4}m = 0.113mm