Question

Two infinite planar sheets are placed parallel to each other. One sheet is uniformly charged with +10 nC/cm^2 and the other with -20nC/cm^2.

A point charge of -5 nC is placed
a) between the sheets
b) in the outside regions.
For each case calculate the strength and show the direction of the electric force experienced by the point charge.

Answer 1

let q = -5 nC

when q is placed between the two plates

electric field due to +10 nc/m^2 = E1 = 10n /2eo towards negative plate

electric field due to -20 nc/m^2 = E2 = 20n /2eo towards negative plate

net electric field = E = 30*10^-9/(2*e0)

E = (30*10^-9)/(2*8.85*10^-12) = 1695 N/C

Force q = F = E*q

F = 1695*5*10^-9 = 8.475*10^-6 N towards    positive plate

+++++++++++++++

part(b)

when q is placed in outside regions

q is placed ouside of +ve sheet

electric field due to +10 nc/m^2 = E1 = (10*10^-9) /2eo away from positive sheet

electric field due to -20 nc/m^2 = E2 = 20n /2eo towards positive sheet

net electric field = E = E2 - E1 = 10*10^-9/(2*e0) towards positive sheet

E = (10*10^-9)/(2*8.85*10^-12)

Force q = F = E*q

F = 2.825*10^-6 N away from positive sheet

q is placed ouside of -ve sheet

electric field due to +10 nc/m^2 = E1 = (10*10^-9) /2eo away from negative sheet

electric field due to -20 nc/m^2 = E2 = 20n /2eo towards negative plate

net electric field = E = E2 - E1 = 10*10^-9/(2*e0) towards negative sheet

E = (10*10^-9)/(2*8.85*10^-12)

Force q = F = E*q

F = 2.825*10^-6 N away from negative sheet