Deflection of electron in electric field

[blue_soda025]

An electron is traveling horizontally at a speed of 8.70 x 10^6 m/s enters an electric field of 1.32 x 10^3 N/C between two horizontal parallel plates as described in the diagram.
Calculate the vertical displacement of the electron as it travels between the plates.

How do I go about solving this? Any help would be appreciated since I have a test tomorrow.

 

[kevinalm]

t=Horizontal length/velocity
f=electron charge*electic field
a=f/electron mass

Then use the formula for x(t) of constant acceleration

This ignores gravity which almost certainly isn't significant, and relativistic effects which are nearly as insignificant as the velocity<<c.

 

[thepatientmental]

To solve this problem, we can use the equation for the force on a charged particle in an electric field, F = qE, where F is the force, q is the charge of the particle, and E is the strength of the electric field.

In this case, we know the speed of the electron (8.70 x 10^6 m/s) and the strength of the electric field (1.32 x 10^3 N/C). We also know that the electron has a charge of -1.6 x 10^-19 C. Plugging these values into the equation, we get:

F = (-1.6 x 10^-19 C)(1.32 x 10^3 N/C) = -2.112 x 10^-16 N

Since the force is in the opposite direction of the electric field, the electron will experience a downward force. This means that the electron will be deflected downwards as it travels between the plates.

To calculate the vertical displacement, we can use the equation for displacement, s = ut + (1/2)at^2, where s is the displacement, u is the initial velocity, t is the time, and a is the acceleration.

Since the electron is initially traveling horizontally, its initial vertical velocity (uy) is 0. The acceleration in the vertical direction (ay) can be calculated using Newton's second law, F = ma, where m is the mass of the electron (9.11 x 10^-31 kg). So we have:

-2.112 x 10^-16 N = (9.11 x 10^-31 kg)ay

Solving for ay, we get:

ay = -2.318 x 10^14 m/s^2

Now, we can plug in the values for uy, ay, and t (which can be calculated using the horizontal velocity and the distance between the plates) into the displacement equation to get the vertical displacement, s:

s = (0)(t) + (1/2)(-2.318 x 10^14 m/s^2)t^2 = -1.159 x 10^14t^2

Therefore, the vertical displacement of the electron is -1.159 x 10^14t^2, where t is the time it takes for the electron to travel between the plates. Keep in mind that this value will be negative since the electron is def