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NEET PHYSICSEasy

Two infinitely long parallel conducting plates having surface charge densities +\sigma and −\sigma respectively, are separated by a small distance. The medium between the plates is a vacuum. If ε₀ is the dielectric permittivity of vacuum, then the electric field in the region between the plates is:

A

0 V/m

B

\sigma /(2ε₀) V/m

C

\sigma /ε₀ V/m

D

2\sigma /ε₀ V/m

Step-by-Step Solution

The electric field due to a single uniformly charged infinite plane sheet is E=σ2ϵ0E = \frac{\sigma}{2\epsilon_0} . For two parallel plates with surface charge densities +σ+\sigma and σ-\sigma:

  1. In the region between the plates, the electric field due to the positive plate points away from it (towards the negative plate), and the field due to the negative plate points towards it (also away from the positive plate).
  2. Since both fields point in the same direction, they add up: Enet=E++E=σ2ϵ0+σ2ϵ0=σϵ0E_{net} = E_+ + E_- = \frac{\sigma}{2\epsilon_0} + \frac{\sigma}{2\epsilon_0} = \frac{\sigma}{\epsilon_0} . (Note: In the outer regions, the fields are opposite and cancel out, resulting in zero electric field).
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