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Consider an electron travelling with a s...

Consider an electron travelling with a speed `V_(0)` and entering into a uniform electric field `vecE` which is perpendicular to `vecV_(0)` as shown in the Figure.

Ignoring gravity, obtain the electron 's acceleration velocity and position as functions of time.

Text Solution

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Speed of an electron `= V_(0)`
Uniform electric field = `vecE`
(a) Electron.s acceleration : Force on electron due to uniform electric F = Ee
Downward acceleration of electron due to electric field a =` (F)/(m) = -(eE)/(M)`
Vector form `veca= -(eE)/(M)hatj`
(b) Electron.s velocity : Speed of electron in horizontal direction u = `V_(0)`
From the equation of motion V= `mu` +at
`V= V_(0)-(eE)/(M)t`
vector form `vecV=V_(0)hatj- (eE)/(M)t hatj`
(c ) Electron.s position : Position of electron s=r
From equation of motion `r= V_(0)t+(1)/(2)(-(eE)/(M))t^(2)`
`r= V_(0)t= (1)/(2)(eE)/(M) t^(2) hatj`
Vector form `vecr= V_(0)t hati -(1)/(2) (eE)/(M) t^(2)hatj`
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