Force, Electric Field, and Positive Particle

[Soaring Crane]

Homework Statement

A long line carrying a uniform linear charge density 50.0 microcoulombs/m runs parallel to and 10.0 cm from the surface of a large, flat plastic sheet that has a uniform surface charge density of -100 microcoulombs/m^2 on one side.

Find the location of all points where an alpha particle would feel no force due to this arrangement of charged objects.
Indicate this location as a distance from the line.

Choose an appropriate location of these points at a distance: above the line or between the line and the sheet.

Homework Equations

E = [1/(2*episilon_0*pi)]*(lambda/r) for wire

E = omega/(2*episilon_0) for sheet (Do I use this formula?)

The Attempt at a Solution

I don’t know if I set this up correctly or used the correct formulas.

E = [1/(2*episilon_0*pi)]*(lambda/r) + omega/(2*episilon_0)

0 = [1/(2*episilon_0*pi)]*(lambda/r) + omega/(2*episilon_0)

-omega/(2*episilon_0) = [1/(2*episilon_0*pi)]*(lambda/r)

r = (lambda)/(-omega*pi) = (50*10^-6 C/m)/[pi -(-100*10^-6 C/m^2)] = 0.1592 m ?

This distance would be above the line because the electric field vectors, which are in same direction as force vectors, on the positive alpha particle would be in opposite directions??

Thanks.

 

[Dick]

It looks fine to me. Is something unclear?

 

[m2003]

I would first like to commend you on your attempt at solving this problem. Your equations and approach are correct, and you have correctly identified the distance above the line as the location where an alpha particle would experience no force.

To further explain, the electric field due to the line and the sheet can be calculated separately using the equations you provided. The electric field due to the line will be directed away from the line, while the electric field due to the sheet will be directed towards the sheet. At the location where the two electric fields cancel out, the net electric field will be zero and the alpha particle will experience no force.

This location will be above the line because, as you correctly stated, the electric field and force vectors for a positive particle are in opposite directions. Therefore, the electric field due to the line must be greater than the electric field due to the sheet in order for them to cancel out. This is why the distance must be above the line, as the electric field due to the sheet will always be directed towards the sheet.

Overall, your solution and understanding of the problem are correct. Keep up the good work!