Question

(1) 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 field, and then extract them as needed. Antimatter annihilates with normal matter, producing pure energy. What strength magnetic field is needed to hold antiprotons, moving at 5.0 x 10^7 m/s in a circular path 2.00 m in radius? Antiprotons have the same mass as protons but the opposite (negative) charge.
(2) Is this field strength obtainable with today’s technology or is it a futuristic possibility?

Answer 1

Solution :

The relationship between the strength of magnetic field and the radiusof a charged particle's path is obtained through Newton's second law, which is given by :

F = ma

F = qvB and $a=\frac{v^2}{r}$

Substituting these values in the second law of Newton,

$qvB=\frac{mv^2}{r}$

Now solving for B, we get:

$B = \frac{mv}{rq}$

  $=\frac{(1.67 \times 10^{-27})(5 \times 10^{7})}{2\times 1.6 \times 10^{-19}}$

 = 0.261 T

The field strength can be obtained by using the technology of today.