# Solve Proton Homework: Min Speed to Miss Lower Plate

• Vanessa Avila
In summary, the conversation discusses a problem involving a proton being projected between two parallel plates with an electrical field. The goal is to find the minimum speed of the proton in order to miss the lower plate as it emerges from the field. The solution involves using the equations q(E) = ma, x = vt, and y = 1/2a(t^2), and taking into account the fact that the proton enters at the midway point between the plates. The final answer is approximately 7.4*10^6 m/s.
Vanessa Avila

## Homework Statement

In the figure, a proton, mass 1.67×10^−27 kg, is projected horizontally midway between two parallel plates that are separated by 0.20cm, with an electrical field with magnitude 7.8×10^5N/C between the plates. If the plates are 5.40cm long, find the minimum speed of the proton that just misses the lower plate as it emerges from the field.

q(E) = ma
x = vt
y = 1/2a(t^2)

## The Attempt at a Solution

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This is what I did:
1.6*10^-19(7.8*10^5) = 1.67*10^-27 (a)
solving for a I get: 7.47*10^13 m/s^2

then i solve for t
2*10^-3 = (1/2)(7.47*10^13)(t^2)
t = sqrt(7.47*10^13/((2)(2*10^-3))
I get 7.32*10^-9 s

then i plug that in the x = vt eqn
0.054/7.23*10^-9 = v
v = 7.4*10^6 m/s

But that is wrong

It says the proton comes in midway, which means y is 0.1cm, not 0.2cm

Xiaochao Zheng said:
It says the proton comes in midway, which means y is 0.1cm, not 0.2cm
Oh I see.Thank you!

## 1. What is the purpose of solving proton homework?

The purpose of solving proton homework is to understand and apply the principles of physics, specifically electric fields and forces, to solve problems related to protons and their interactions with other charged objects.

## 2. How do you calculate the minimum speed required for a proton to miss the lower plate?

To calculate the minimum speed required for a proton to miss the lower plate, you need to use the equation: v = sqrt(2qV/m), where v is the minimum speed, q is the charge of the proton, V is the potential difference between the plates, and m is the mass of the proton. Plug in the values and solve for v.

## 3. Can you explain why the minimum speed needed for the proton to miss the lower plate is independent of its initial velocity?

The minimum speed required for the proton to miss the lower plate is independent of its initial velocity because it is solely dependent on the potential difference between the plates and the charge and mass of the proton. The initial velocity of the proton does not affect these factors and therefore does not affect the minimum speed.

## 4. How does the distance between the plates affect the minimum speed required for the proton to miss the lower plate?

The distance between the plates does not directly affect the minimum speed required for the proton to miss the lower plate. However, it does affect the potential difference between the plates, which in turn affects the minimum speed. A greater distance between the plates will result in a smaller potential difference and therefore a lower minimum speed.

## 5. What other factors can affect the minimum speed needed for the proton to miss the lower plate?

Other factors that can affect the minimum speed needed for the proton to miss the lower plate include the charge and mass of the proton, the potential difference between the plates, and any external forces acting on the proton. Changes in these factors can alter the minimum speed required for the proton to miss the lower plate.

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