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An ion of mass 1. 8 xx 10 ^(-27) kg car...

An ion of mass `1. 8 xx 10 ^(-27) ` kg carrying a charge `2 xx 10 ^(- 16) C` after being accelerated through a potential difference of 200 V enters a uniform magnetic field of intensity `2 xx 10 ^(-3) T bot r ` to the direction of motion. Calculate the radius of the path described by the ion.

Text Solution

Verified by Experts

`m = 1*8 xx 10^(-29)` kg
`q = 2 xx 10^(-18)` C
`V = 100` volt
`B = 10^(-3)` T
Radius ` = r = ?`
`(1)/(2)mv^(2) = qV`
`v = sqrt((2qV)/(m))`
`v = sqrt((2 xx 2 xx 10^(-18) xx 100)/(1*8 xx 10^(-29)))`
` = sqrt(2*22 xx 10^(13))`
` = sqrt(22*2 xx 10^(12))`
But ` r = (mv)/(Bq)`
`r = (1*8 xx 10^(-29) xx 4*71 xx 10^(6)) xx 2 xx 10^(-18)`
`r = 4*24 xx 10^(-2)` m
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