To solve this problem we must keep in mind the concepts related to angular kinematic equations. For which the angular velocity is defined as
Where
Final angular velocity
Initial angular velocity
Angular acceleration
t= time
In this case we do not have a final angular velocity, then
Re-arrange for
Therefore the mangitude of the angular aceleration is 5449.1rad/s²
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.