Determine the accelration of a relativistic electron moving along a unifrom electric field of strength `E` at the moment when its kinetic energy becomes equal to `T`.

Explanation

As before, `T = e E x`
Now in linear motion,
`(d)/(dt) (m_(0) v_(x))/(sqrt(1 - v^(2)//c^(2))) = (m_(0) w)/(sqrt(1 - v^(2)//c^(2))) + (m_(0) w)/((1 - v^(2)//c^(2))^(3//2)) = (v)/(c^(2)) w`
`= (m_(0))/((1 - v^(2)//c^(2))^(3//2))w = ((T + m_(0) c^(2))^(3))/(m_(0)^(2) c^(6)) w = e E`,
So, `w = (e E m_(0)^(2) c^(6))/((T + m_(0) c^(2))^(3)) = (e E)/(m_(0)) (1 + (T)/(m_(0) c^(2)))^(-3)`