Q.Consider an electron travelling with a speed $v_0$ 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 $t$.

Step 1. The electron (charge $-e$) enters with velocity $v_0\hat{\imath}$ into a uniform field $\vec{E}=E\hat{\jmath}$ perpendicular to $v_0$; the force on it is $\vec{F}=(-e)\vec{E}=-eE\hat{\jmath}$, so the acceleration is $\vec{a}=\vec{F}/m=-\dfrac{eE}{m}\hat{\jmath}$, constant and perpendicular to the initial velocity.

Step 2. With no force along $\hat{\imath}$, the $x$-velocity stays constant at $v_0$; along $\hat{\jmath}$, the velocity grows uniformly from zero under the constant acceleration: $\vec{v}(t)=v_0\hat{\imath}-\dfrac{eE}{m}t\,\hat{\jmath}$. …

Apply Newton's second law with F = -eE to get a constant acceleration, then integrate twice, treating this …

• Forgetting the electron's charge is negative, which determines the direction of the deflection relative to E. …