Calculating Electric Field & Proton Acceleration

[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?

 

[Delphi51]

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?