A long line carrying a uniform linear charge density +57.0 µC/m runs parallel to

Question

A long line carrying a uniform linear charge density +57.0 µC/m runs parallel to and 10 cm from the surface of a large, flat plastic sheet that has a uniform surface charge density of -120 µC/m2 on one side. Find the location of all points on a line perpendicular to the sheet and the charged line where an particle would feel no force due to this arrangement of charged objects.

15.2 cm from the line (in either direction)

15.1 cm from the line (in either direction)

15.15 cm from the line (in either direction)

15.06 cm from the line (in either direction)

Explanation / Answer

field due to infinite sheet of charge = sigma/ 2e0

                            = (120 x 10^-6) / (2 x 8.854 x 10^-12)

                     = 6776598.15 N/C

this is towards the sheet and constant irrespective of distance from sheet.

field due to a long line of charge = 2 k lambda / r

          = (2 x 9 x 10^9 x 57 x 10^-6) / r

to make field zero.

6776598.15 = (2 x 9 x 10^9 x 57 x 10^-6) / r

r = 0.1512 m = 15.12 cm from line charge.

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