Viewers of Star Trek hear of an antimatter drive on the Starship Enterprise. One possibility for such a futuristic energy
source is to store antimatter charged particles in a vacuum chamber, circulating in a magnetic eld, and then extract them
as needed. Antimatter annihilates with normal matter, producing pure energy. What strength magnetic eld is needed to
hold antiprotons, moving at 5.00×107 m/s in a circular path 2.00 m in radius? Antiprotons have the same mass as protons
but the opposite (negative) charge. (b) Is this eld strength obtainable with today’s technology or is it a futuristic
possibility?

a) 0.261 T

b) this field strength is obtainable with today's technology

Explanation:

a)

The force experienced by a charged particle moving perpendicular to a magnetic field is given by

where

q is the charge

v is the velocity

B is the strength of the field

This force is perpendicular to the motion of the particle, which therefore moves in a circular path; and so, this force acts as centripetal force, so we can write:

where

m is the mass of the particle

r is the radius of the circle

In this problem, we have:

(magnitude of the charge of antiprotons)

(velocity)

(mass of antiprotons)

r = 2.00 m (radius)

Therefore, we can re-arrange the equation and solve to find B, the magnetic field strength:

B)

The strength of the magnetic field calculated in part A) is

This is indeed a very strong magnetic field. In fact, by comparison, the Earth's magnetic field has a strength of about

However, there are current technologies available that are able to produce such strong fields. For instance, the superconducting magnets in the LHC (Large Hadron Collider) are able to produce magnetic fields of strength up to 8 Tesla (8 T).

Therefore, we can say that this field strength is obtainable with today's technology.

e/c, where e is its total energy