An antiproton is identical to a proton except it has the opposite charge, âˆ’e. To study antiprotons, they must be confined in an ultrahigh vacuum because they will annihilateâˆ’producing gamma raysâˆ’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 Ã— 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 = _________

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

[tex]r = \frac{mv}{Bq} \\\\r=\frac{mv}{Bq} \\\\r=\frac{1.67 \times 10^-^2^7\times 1.5 \times 10^4}{4.5 \times 10^-^3\times 11.6\times 10^-^1^9} \\\\r=347.9\times 10^-^4\\\\r=3.479cm[/tex]

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