Motion In Electric Field

Two parallel metal plates $A$ and $B$ carrying equal and opposite charges are placed in vacuum, tilted at angle $\theta$ above the horizontal. A small charged ball of mass $m = 1$ g and charge $q = 1.41 \times 10^{-4}$ C enters the field through a hole $P$ on plate $A$ with horizontal velocity $v_0 = 0.1$ m/s. After $t = 0.02$ s in the field, the ball has not touched plate $B$ and has returned to point $P$. Take $g = 10\ \mathrm{m/s^2}$.

Three small balls of equal mass --- one positively charged, one negatively charged, and one uncharged --- are launched with the same velocity from point $P$ between two charged horizontal parallel plates, perpendicular to the electric field direction. The upper plate is negative and the lower plate is positive. The three balls land at points $A$, $B$, $C$ on the positive (lower) plate, with $A$ being the farthest horizontal distance from $P$, then $B$, then $C$ (closest to $P$). Gravity is included.

As shown, an electron enters a uniform electric field at point $A$ with velocity $v_0 = 10^{6}$ m/s, directed perpendicular to the field. The electron exits at point $B$ with its velocity at an angle of $30^\circ$ relative to the entry direction. The electron has charge $e = 1.6 \times 10^{-19}$ C and mass $m = 9.1 \times 10^{-31}$ kg.

A charged particle of mass $m = 5 \times 10^{-8}$ kg enters horizontally at the central midline between two horizontal parallel metal plates $A$ (top) and $B$ (bottom) with initial speed $v_0 = 2$ m/s. The plate length is $l = 0.1$ m and the plate separation is $d = 2 \times 10^{-2}$ m. When $U_{AB} = 1000$ V, the particle traverses the field along a straight horizontal line. Take $g = 10\ \mathrm{m/s^2}$.