Consider an electron travelling with a speed V_{Φ} and entering into a uniform electric field `vec"E"` which is perpendicular to `vec"V"_0` as shown in the Figure. Ignoring gravity, obtain the electron’s acceleration, velocity and position as functions of time.

#### Solution

Speed of an electron = V_{0}

Uniform electric field = `vec"E"`

**(а) Electron’s acceleration:**

Force on electron due to uniform electric field, F = Ee

Downward acceleration of electron due to electric field, a = `"F"/"m"`

`= - "eM"/"M"`

Vector from, `vec"a" = - "eM"/"M" hat"j"`

**(b) Electron’s velocity:**

Speed of electron in horizontal direction, u = V_{0} From the equation of motion, V = u + at

V = `"V"_0 "eM"/"M" "t"`

Vector from `vec"V" = "V"_0 hat"j" - "eM"/"M" "t" hat"j"`

**(c) Electron’s position:**

Position of electron, s = r

From equation of motion, r = V_{0} t + `1/2 (- "eM"/"M")"t"^2`

r = V_{0} t + `1/2 "eM"/"M" "t"^2 hat"j"`

Vector from,

`vec ""r" = "V"_0 "t" hat "j" 1/2 "eM"/"M" "t"^2 hat"j"`