An electron is accelerated in an electric field of intensity `E = 3.0 xx 10^(6)` N /C. Find the speed of the electron after 1.0 ns. What would be the speed of the electron, if 'its mass is independent of speed?

Answer

`2.6xx10^(8)m//s;5.3xx10^(8)m//s`

Explanation

The electron velocity may be found from the formula (13.2)
`u=("lt")/(sqrt(1+b^(2)t^(2)//c^(2)))`
Here `b=F//m_(0)=eE//m_(0).` For an electron `e=1.6xx10^(-19)Cm_(e)=9.1xx10^(-31)kg`. We have
`b=(1.6xx10^(-19)xx3.0xx10^(6))/(9.1xx10^(-31))=5.3xx10^(17)m//s^(2)`
`(bt)/c-(5.3xx10^(17)xx10^(-9))/(3.0xx10^(8))=1.76`
`u=(bt)/(sqrt(1+b^(2)t^(2)//c^(2)))=(5.3xx10^(17)xx10^(-9))/(sqrt(1+1.76^(2)))=(5.3xx10^(8))/(2.0)=2.6xx10^(8)` m/s
If there is no relativistic mass increase, the electron velocity reaches the value
`u=(eEt)/(m_(0))~~(1.6xx10^(-19)xx3.0xx10^(9)xx10^(-9))/(9.1xx10^(-31))=5.3xx10^(8)m//s`
i.e. the velocity computed with the aid of the formulas of Newtonian mechanics exceeds the maximum velocity.