Answer:
0.00645 m
Explanation:
m = Mass of lithium = [tex]1.16\times 10^{-26}\ kg[/tex]
V = Voltage = 290 V
r = Radius of path
B = Magnetic field = 0.710 T
q = Charge of electron = [tex]1.6\times 10^{-19}\ C[/tex]
v = Velocity of mass
The kinetic energy in moving a charge and the work done by the charge will balance each other
[tex]\frac{1}{2}mv^2=qV\\\Rightarrow v=\sqrt{\frac{2qV}{m}}\\\Rightarrow v=\sqrt{\frac{1\times 1.6\times 10^{-19}\times 290}{1.16\times 10^{-26}}}\\\Rightarrow v=63245.5532\ m/s[/tex]
The velocity by which the charge is moving is 63245.5532 m/s
The force on moving a charge and the centripetal force will balance each other
[tex]F=F_c\\\Rightarrow Bqv=m\frac{v^2}{r}\\\Rightarrow r=\frac{mv}{Bq}\\\Rightarrow r=\frac{1.16\times 10^{-26}\times 63245.5532}{0.71\times 1.6\times 10^{-19}}\\\Rightarrow r=0.00645\ m[/tex]
The radius of the magnetic field is 0.00645 m
