Charge density of a infinite straight wire

[caheobong]

Hi, I am new to this forum. I have a question on one of the physics problem.
a proton is shot with a speed v from the point a in the vicinity of a infinite straight wire carrying a charge density. in term of these variables determine the nearest distance of approach.

Homework Equations

Ki+Ui=Kf +Uf
Ui=0, Kf=0
U= (K*q1*q2)/d

The Attempt at a Solution

so this is what I have done so far:
first I set Ki+Ui=Kf+Uf
since Ui=0, Kf=0 then
Ki=Uf
Ki= (1/2)*m*(v^2) ( m is mass of proton)
Uf= (k*q1*q2)/d ( d is the distance we looking for, q1=e proton, q2= charge density *L)
set Uf=Ki and solve for d
d= (e * charge density * L)/ ( mass of proton * (V^2) * 2 * pi * Eo)

This is my attempt how to solve this problem. however this is an infinite charge wire, the result should not depend on L the length of the wire. So please help me. any hints will help.Thank you so much.

 

[SammyS]

It looks like some important details are missing:

Is the proton shot directly at the line charge? (Then the line charge must be positive for the question to make sense.)

If so, is its path perpendicular to the line charge?

If not, then there are details missing regarding the direction of the initial velocity relative to the location of the line charge. Also, the sign of the line charge would need to be specified.​

U = kq₁q₂d is the potential energy for two point charges, q₁, q₂, separated by distance d.

What is the difference in electric potential at distances d_initial & d_other from an infinite line charge, with linear density, λ ?

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[caheobong]

In the picture, the proton is shot directly toward the charged line, maybe perpendicular

 

[SammyS]

In the picture, the proton is shot directly toward the charged line, maybe perpendicular

That's what I would expect, both directly toward the charged line, and perpendicular to it.

Do you know how electric potential varies with distance from an infinitely long line charge? If not, do you know how electric field varies with distance from an infinitely long line charge?

 

[rwisz]

Hi there! Welcome to the forum. Your attempt at solving the problem is a good start. To find the nearest distance of approach, we can use the conservation of energy equation: Ki + Ui = Kf + Uf. Since the initial potential energy (Ui) is zero and the final kinetic energy (Kf) is also zero (since the proton will come to a stop at its closest approach), we can simplify the equation to: Ki = Uf. We can also substitute in the expression for potential energy: Uf = (k*q1*q2)/d. So now we have: Ki = (k*q1*q2)/d. We know the initial kinetic energy (Ki) since it is given in the problem as (1/2)*m*(v^2). So we can substitute that in as well: (1/2)*m*(v^2) = (k*q1*q2)/d. Now we can solve for d: d = (k*q1*q2)/((1/2)*m*(v^2)). This is the nearest distance of approach for the proton. We can see that it does not depend on the length of the wire, as expected for an infinite wire. I hope this helps!