Question

Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude \(17.0 × 10^{−22} Cm^{-2}\). What is E: 
(a) in the outer region of the first plate, 
(b) in the outer region of the second plate, and (c) between the plates?

Answer 1

The situation is represented in the following figure.
                                       
A and B are two parallel plates close to each other. Outer region of plate A is labelled as \(I\), outer region of plate B is labelled as \(III\), and the region between the plates, A and B, is labelled as \(II\).
Charge density of plate A, \(σ =\, 17.0 × 10^{−22} Cm^{-2}\)
Charge density of plate B, \(σ = −17.0 × 10^{−22} Cm^{-2}\)
In the regions, \(I\) and \(III\), electric field E is zero. This is because charge is not enclosed by the respective plates.
Electric field E in region \(II\) is given by the relation,
                                                               \(E = \frac{σ }{ ε_0}\)
Where, 
\(ε_0\) = Permittivity of free space = \(8.854 × 10^{-12} N^{-1}C^2m^{-2}\)
                                                             \(E = \frac{17.0 × 10^{-22} }{ 8.854 × 10^{-12}}\)
\(= 1.92 × 10^{-10} NC^{-1}\)
Therefore, electric field between the plates is \(1.92 × 10^{-10} NC^{-1}\).