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.
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??