Question

An ion jet is accelerated by a potential difference of 10000 V, before entering a magnetic field of 1T. If the ions describe a circular path of 5 cm radius, determine the charge-mass relationship.

Answer 1

Ratio of charge to mass is 8 x 10⁶

Step-by-step explanation:

q = charge on the ion

V = potential difference = 10000 Volts

B = magnitude of magnetic field = 1 T

m = mass of the ion

`v` = speed gained by the ion due to potential difference

using conservation of energy

kinetic energy gained by ion = electric potential energy lost

`(0.5)mv^(2)=qV`

`mv^(2) = 2qV` eq-1

r = radius of the circular path described = 5 cm = 0.05 m

radius of circular path is given as

`r = (mv)/(qB)`

taking square both side

`r^(2) = (m^(2)v^(2))/(q^(2)B^(2))`

using eq-1

`r^(2) = (2mqV)/(q^(2)B^(2))`

`r^(2) = (2mV)/(qB^(2))`

`(q)/(m) = (2V)/(r^(2)B^(2))`

inserting the values

`(q)/(m) = (2(10000))/((0.05)^(2)(1)^(2))`

`(q)/(m)` = 8 x 10⁶

Ratio of charge to mass is 8 x 10⁶