# Determining the electron speed in parallel plates

• ProAgnusDei
In summary: So, when I plug that in, I get a velocity of 5.31 x 10^6 m/s at tx and 5.45 x 10^6 m/s at tP. In summary, two parallel plates labelled W (negative) and X (positive) are separated by 5.2 cm with an electric potential between them of 150V. An electron starting from rest at time tw reaches plate X at time tx and continues through an opening to reach point P at time tP. The speed at tx is 5.31 x 10^6 m/s and at tP is 5.45 x 10^6 m/s. Using the equations V = kq1/r, Δ
ProAgnusDei

## Homework Statement

Two parallel plates labelled W (negative) and X (positive) are separated by 5.2 cm. The electric potential between the plates is 150 V. An electron starts from rest at time tw and reaches plate X at time tx. The electron continues through an opening in plate X and reaches point P at time tP. Determine the speed at tx and tP

e = -1.6 x 10-19 C
me = 9.1 x 10-31

V = kq1 / r
ΔV = ΔE/q
ε = ΔV / r
Ek = 0.5mv2

## The Attempt at a Solution

I'm not sure how to determine v at tw and tx, but I did find the field strength: ε = 2884.6. We also know the electron starts from rest, so we could use the conservation of energy law to generate the following eq'n.

v2 = 2m-1kq1q2(ra-2 - rb2). But we don't have a "q2" so I'm quite lost. Any help is appreciated!

God bless and thanks!

The Volt is a name given to the unit combination Joules/Coulomb

You should be able to find (in your notes or text) an expression for the work done on a charge falling through a potential difference. The work done shows up as kinetic energy...

You can start by finding the acceleration of the electron.
F = ma = qE
a = qE/m
Then it's a kinematics problem
vf^2 = 2*a*x Thats good for finding Vx

I used your equation (not on my eq'n sheet), a = qE/m, substituted Vq for E, leaving me with Vq˄2 / m. I found acc. to be 3.376 x 10^-6.

Plugged that into eq'n v22 = v12 + 2ad,

which reduces to v2 = sqr(2ad), and I got a velocity (vx) of 5.93 x 10^-4 m/s which seems really slow to me.

ProAgnusDei said:
I used your equation (not on my eq'n sheet), a = qE/m, substituted Vq for E, leaving me with Vq˄2 / m. I found acc. to be 3.376 x 10^-6.
Why would you substitute Vq for E? E here would be the electric field strength (units of [N]/[C] or [V]/[m]). You calculated the electric field strength previously, calling it ε.

However, a more slick approach is to use q*ΔV, with q being the charge on the electron and ΔV the change in electric potential (the 150V). The units are then [C][J]/[C] → [J], which is energy. That's the work done on the electron as it falls through the field...

Ok that makes more sense. When you wrote E, I figured you meant energy, not ε. Tak.

## 1. What is "Determining the electron speed in parallel plates"?

"Determining the electron speed in parallel plates" is a scientific experiment or calculation that involves measuring the speed of electrons between two parallel plates. This can be done using various methods, such as using an electric field or measuring the time it takes for electrons to travel a known distance.

## 2. Why is it important to determine the electron speed in parallel plates?

Determining the electron speed in parallel plates is important because it helps us understand the behavior of electrons in an electric field. This information is crucial in fields such as electronics, where the movement of electrons plays a key role in the functioning of devices.

## 3. What factors affect the electron speed in parallel plates?

The speed of electrons in parallel plates can be affected by various factors, such as the strength of the electric field, the distance between the plates, and the material of the plates. Other external factors, such as temperature and pressure, can also have an impact on electron speed.

## 4. How is the electron speed calculated in parallel plates?

The electron speed in parallel plates can be calculated using the formula v = E/m, where v is the speed, E is the electric field strength, and m is the mass of the electron. This formula takes into account the force exerted on the electron by the electric field and the mass of the electron.

## 5. What are some real-world applications of determining electron speed in parallel plates?

The knowledge gained from determining electron speed in parallel plates has many practical applications. For example, it is crucial in the design and functioning of electronic devices such as computers, televisions, and smartphones. It is also used in particle accelerators and other advanced scientific equipment.

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