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 1.5 × 10^4 m/s and then trapped in a 4.5 mT magnetic field. What minimum diameter must the vacuum chamber have to allow these antiprotons to circulate without touching the walls?Express your answer with the appropriate units. d =

Explanation:

We know that, the force responsible for circulating in circular path is the centripetal force given by the force on charged particle due to magnetic field.

Here the charge is antiproton is

p = -1.6 * 10⁻¹⁹C

the speed of proton is given by 1.5 * 10 ⁴ m/s

the magnetic field is B = 4.5 * 10⁻³T

we have force due to magnetic field is equal to centripetal force

Bqv = mv² / r

Bq = mv / r

The diameter d of the vacuum chamber have to allow these antiprotons to circulate without touching the walls is

d = 2r

d = 2 * 3.479

d = 6.958

d ≅ 7cm

force is mass*acceleration.

we have a very small mass: 11.4*0.001 kg

if we want 0.035n of force, we need an acceleration:

0.035 = 11.4*0.001*a

a = 0.035/(11.4*0.001) m/s^2

neither accurate nor precise.