# Proton deflection in a capacitor

In summary, a proton with a speed of 1.0*106 m/s enters a 2.0-cm-wide parallel-plate capacitor with surface charge densities of 1*10^-6 C/m2 on the plates. The question asks for the distance the proton is deflected sideways when it reaches the far edge of the capacitor, assuming a uniform electric field inside and zero outside. To solve this, the equation d=.5at2 can be used, with the acceleration in the y direction and the displacement in millimeters. Kinematics equations can also be applied in both the x and y directions, with the final answer in millimeters.

## Homework Statement

A proton traveling at a speed 1.0*106 m/s of enters the gap between the plates of a 2.0-cm-wide parallel-plate capacitor. The surface charge densities on the plates are 1*10^-6 C/m2.

How far has the proton been deflected sideways when it reaches the far edge of the capacitor? Assume the electric field is uniform inside the capacitor and zero outside.

d=.5at2

## The Attempt at a Solution

1*10-4

Thread moved to Intro Physics.

Welcome to the PF, badBKO. Could you please show us more of your work, including units? What force creates the sideways acceleration? How do you calculate the magnitude of that force?

The force that moved it to the right is not needed. There is no acceleration in the x deminsion, on lay in the y. The ending answer should be in millimeters of displacement.

I tried using kinematics in 2 dimension x and y
x1, y1, t1, etc

and the equations

y1 = y0 + vy(t1-t0) + .5ay(t1-t0)2

used the same equation for the x variable also.

## 1. How does a capacitor deflect protons?

A capacitor consists of two parallel plates with opposite charges. When a proton enters the electric field between the plates, it will experience a force due to the electric field. The direction of this force will depend on the charge of the proton and the direction of the electric field. This force will cause the proton to deflect towards the positively charged plate.

## 2. What factors affect the degree of proton deflection in a capacitor?

The degree of proton deflection in a capacitor depends on the strength of the electric field, the charge of the proton, and the distance between the plates. A stronger electric field or a higher charge on the proton will result in a greater deflection. A larger distance between the plates will also lead to a greater deflection.

## 3. Why are protons deflected in a capacitor?

Protons are deflected in a capacitor due to the electric force they experience in the electric field between the plates. This force is perpendicular to the direction of motion of the proton, causing it to change direction and deflect towards the positively charged plate.

## 4. How can the deflection of protons in a capacitor be used in scientific experiments?

The deflection of protons in a capacitor can be used in scientific experiments to study the properties of electric fields and to measure the charge of particles. It can also be used in particle accelerators to manipulate the path of particles and study their interactions.

## 5. What is the difference between deflection of protons in a capacitor and in a magnetic field?

The deflection of protons in a capacitor is caused by the electric force, while the deflection in a magnetic field is caused by the magnetic force. The direction of deflection is also different - in a capacitor, the protons are deflected towards the positively charged plate, while in a magnetic field, they are deflected perpendicular to the direction of motion. Additionally, the strength of the deflection is affected by different factors in each case - the electric field and the magnetic field have different strengths and depend on different physical properties.

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