Answer:
Ratio of charge to mass is 8 x 10⁶
Explanation:
q = charge on the ion
V = potential difference = 10000 Volts
B = magnitude of magnetic field = 1 T
m = mass of the ion
[tex]v[/tex] = speed gained by the ion due to potential difference
using conservation of energy
kinetic energy gained by ion = electric potential energy lost
[tex](0.5)mv^{2}=qV[/tex]
[tex]mv^{2} = 2qV[/tex] eq-1
r = radius of the circular path described = 5 cm = 0.05 m
radius of circular path is given as
[tex]r = \frac{mv}{qB}[/tex]
taking square both side
[tex]r^{2} = \frac{m^{2}v^{2}}{q^{2}B^{2}}[/tex]
using eq-1
[tex]r^{2} = \frac{2mqV}{q^{2}B^{2}}[/tex]
[tex]r^{2} = \frac{2mV}{qB^{2}}[/tex]
[tex]\frac{q}{m} = \frac{2V}{r^{2}B^{2}}[/tex]
inserting the values
[tex]\frac{q}{m} = \frac{2(10000)}{(0.05)^{2}(1)^{2}}[/tex]
[tex]\frac{q}{m}[/tex] = 8 x 10⁶
Ratio of charge to mass is 8 x 10⁶
