Without completing the calculations, determine what the new volume will be in the problem below. Also, explain how you were able
1 answer:
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Answer:
0.092 m
Explanation:
A charged moving particle immersed in a region with magnetic field follows a circular trajectory at constant speed (uniform circular motion), since the magnetic forces acts perpendicular to the direction of motion of the particle.
Since the magnetic force acts as centripetal force, we can write:
where
q is the charge of the particle
v is its velocity
B is the strength of the magnetic field
m is the mass of the particle
r is the radius of the orbit
Solving the equation for r,
For the ion of oxygen-16, we have:
(it is singly charged)
So the radius of its orbit is
For the ion of oxygen-18, we have:
(it is singly charged)
So the radius of its orbit is
After each ion has travelled a semicircle, the separation between the two ions will be twice the difference in their radius, so:
The difference in electric potential energy between the two points is
where q is the magnitude of the charge and
is the electric potential difference.
But for energy conservation, the difference in electric potential energy
between the two points is equal to the work done to move the charge between A and B:
so we have
and by substituting the numbers of the problem, we find the value of:
where q is the magnitude of the charge and
But for energy conservation, the difference in electric potential energy
so we have
and by substituting the numbers of the problem, we find the value of