Answer :
Answer:
The mass is [tex]m =6.4*10^{-28} \ kg[/tex]
Explanation:
From the question we are told that
The speed of the charge is [tex]v = 1.0 *10^{6} \ m/s[/tex]
The magnetic field is [tex]B = 0.20 \ T[/tex]
The radius is [tex]r = 0.02 \ m[/tex]
The value of the charge is [tex]e = 1.60 *10^{-19} \ C[/tex]
The centripetal acting on the charge moving in the circular orbit is mathematically represented as
[tex]F_c = \frac{mv^2}{r }[/tex]
Now this centripetal force is due to the force exerted on the charge by the magnetic field on the charge which is mathematically represented as
[tex]F_m = qv B sin\theta[/tex]
At the maximum of this magnetic force [tex]\theta = 90 ^o[/tex]
So
[tex]F_m = e v B sin(90)[/tex]
[tex]F_m = e v B[/tex]
Now given that it is this magnetic force that is causing the circular motion we have that
[tex]F_c = F_m[/tex]
=> [tex]\frac{mv^2}{r } = ev B[/tex]
=> [tex]m = \frac{e * B * r }{v }[/tex]
substituting values
[tex]m = \frac{ 1.60 *10^{-19} * 0.20 * 0.020 }{1.0*10^{6} }[/tex]
[tex]m =6.4*10^{-28} \ kg[/tex]