Respuesta :
Answer:
[tex]d=7.578\,cm[/tex]
Explanation:
Given:
- mass of the one ion, [tex]m_1=9.9\times 10^{-27}\,kg[/tex]
- mass of another ion, [tex]m_2=2.7\times 10^{-26}\,kg[/tex]
- velocity of projection into the magnetic field, [tex]v=71000 \,m.s^{-1}[/tex]
- charge on each ion, [tex]q_1=q_2=1.60218\times 10^{-19}C[/tex]
- magnetic field, [tex]B=0.1 \,T[/tex]
We have, force on a charged particle due to the perpendicular magnetic field:
[tex]F=q.v.B[/tex]............................(1)
Force on mass moving in a circular trajectory
[tex]F=\frac{m.v^2}{r}[/tex]...............................(2)
where "r" is the radius of trajectory.
from eq. (1) & (2)
[tex]m.v=q.B.r[/tex]
putting the values for the condition 1:
[tex]9.9\times 10^{-27}\times 71000= 1.60218\times 10^{-19}\times 0.1\times r_1[/tex]
[tex]r_1=0.04387\,m[/tex]
[tex]r_1=4.387\,cm[/tex]
putting the values for the condition 2:
[tex]2.7\times 10^{-26}\times 71000= 1.60218\times 10^{-19}\times 0.1\times r_2[/tex]
[tex]r_2=0.11965\,m[/tex]
[tex]r_2=11.965\,cm[/tex]
∵The charges have covered a semicircular path from the point of entrance,
∴ their difference in the radius will give their distance from each other.
[tex]d=r_2-r_1[/tex]
[tex]d=11.965-4.387[/tex]
[tex]d=7.578\,cm[/tex]
