Consider two infinitely large plane parallel conducting plates as shown below [the two plates are vertical and face each other, and the point charge sits on the line joining them at d/2 from each]. The plates are uniformly charged with surface charge densities +σ and -2σ. The force experienced by a…

Question

Consider two infinitely large plane parallel conducting plates as shown below [the two plates are vertical and face each other, and the point charge sits on the line joining them at d/2 from each]. The plates are uniformly charged with surface charge densities +σ and -2σ. The force experienced by a point charge +q placed at the mid-point between the two plates will be

Accepted Answer

(4) (3σ q)/(2ε₀). Each infinite sheet produces a uniform field of magnitude (|σ|)/(2ε₀) on either side, independent of distance. In the region between the plates the positive sheet pushes +q away from itself and the negative sheet pulls +q towards itself, so the two fields point the SAME way and add. E=σ/(2ε₀)+(2σ)/(2ε₀)=(3σ)/(2ε₀). F=qE=(3σ q)/(2ε₀), directed from the +σ plate towards the -2σ plate. (The mid-point position is irrelevant, since the field is uniform.)

Step-by-step solution

Why the other options are wrong