# 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.