Task:
Get the equation that describes the trajectory of electrons in the electric field of a plate capacitor.

Method: Combine the shown equtions to a y(x)-equation.

y(x) =

Hint 1: In the y(x)-equtation you must replace t by another expression.

Hint 2: Solve the equation $$x(t)=v_0\cdot t$$ for t and put this in $$y(t)=\frac{1}{2}a_y\cdot t^2$$

Kinematic Equation for x-component

Kinematic Equation for y-component

$x(t)=v_0\cdot t$

$y(t)=\frac{1}{2}a_y\cdot t^2$

Useable variables:

x = position on x-axis
v0 = velocity in x-direction
ay = accelertation in y-direction

Typing tips:

x² must be typed as x*x
2x must be typed as 2*x

Please note the following :

Useable variables:

x = position on x-axis
v0 = velocity in x-direction
ay = accelertation in y-direction
Va = acceleration voltage
Vp = capacitor voltage
e = charge of an electron
m = mass of an electron
d = distance between capcitor plates

Typing tips:

x² must be typed as x*x
2x must be typed as 2*x

Correct! As you can see on the overlay of plot and experiment your input is correct. Modify acceleration or deflection voltage and see, that plot and electron path alsways match.

1. Step: Solve $x(t) =v_0\cdot t$ for t.$$ \Rightarrow t=\frac{x}{v_0}$$ 2. Step: Plug in that in$y(t)=\frac{a_y}{2}\cdot t^2$.$$ \Rightarrow y(x)=\frac{a_y}{2}\cdot \frac{x^2}{{v_0}^2}$$3. Step: Type solution in input lines.