# Calculating Electric Field & Proton Acceleration

• yjk91
In summary, the conversation discusses the calculation of the magnitude of electric field and acceleration at a specific point in space due to a wire with a certain number of electrons and length. The conversation also includes the use of Coulomb's law and force equations to find the answers. However, the details of the calculation are not provided, making it difficult to determine the accuracy of the attempted solution. Further clarification and a diagram may be necessary to fully understand the problem and arrive at the correct answer.
yjk91

## Homework Statement

A total of 3.22 106 electrons are placed on an initially uncharged wire of length 1.29 m.

(a) What is the magnitude of the electric field a perpendicular distance of 0.396 m away from the midpoint of the wire?

(b) What is the magnitude of the acceleration of a proton placed at that point in space?

## The Attempt at a Solution

A total of 2.82 * 10^6 electrons are placed on an initially uncharged wire of length 1.34 m.
(a) What is the magnitude of the electric field a perpendicular distance of 0.404 m away from the midpoint of the wire?

so i did
2.82 X 10^6 electrons X 1.6 X 10^-19 C = 4.512 * 10 ^-13 = q

then i used E = K*q / r^2

E = 2 integral( k*q / r^2, min .404, max .78 (the hypot))
and got 0.00969 but the answer is 0.0128 n/C

mmm a little offf any suggestions?

(b) What is the magnitude of the acceleration of a proton placed at that point in space?
Newtons famous law Force = mass*accel
Look up the mass of a proton
a = F/m
does this look right?

Your part (a) is missing a lot of detail; I can't tell if it is right without doing all the work! In Integral k*dq/r², what did you replace dq with? Say you use λ = q/1.34 as the charge density along the wire. Then dq = λ*dx would work. But your integral is now over x, so r² has to be expressed in terms of x. Also, the horizontal components of the dE vectors cancel out, so you must put in a cosine or sine to take only the vertical component. I think a diagram is required to make sense of what is vertical and what is horizontal. Did you do all that?

## What is an electric field?

An electric field is a physical quantity that describes the influence of an electric charge on other charges in its vicinity. It is a vector field, meaning it has both magnitude and direction, and is created by the presence of electric charges.

## How do you calculate the electric field?

The electric field can be calculated by dividing the force exerted on a test charge by the magnitude of the charge. Mathematically, it can be expressed as E = F/q, where E is the electric field, F is the force, and q is the magnitude of the test charge.

## What is proton acceleration?

Proton acceleration is the process of increasing the speed of a proton by applying a force to it. This is typically done using an electric field, which accelerates the positively charged proton in the direction of the field.

## How do you calculate proton acceleration?

Proton acceleration can be calculated using the formula a = F/m, where a is the acceleration, F is the force, and m is the mass of the proton. The force can be determined by multiplying the electric field strength by the charge of the proton.

## What are some real-world applications of calculating electric field and proton acceleration?

Calculating electric field and proton acceleration is essential in understanding and designing various technologies such as particle accelerators, medical imaging techniques, and electronic devices. It is also crucial in studying the behavior of charged particles in space and in developing new energy sources, such as nuclear fusion.

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