Question

Consider two infinitely large plane parallel conducting plates as shown below. The plates are uniformly charged with a surface charge density and . The force experienced by a point charge +q placed at the mid point between two plates will be:

Answer 1

$\frac{q\sigma}{\epsilon_0}$

Answer 2

The electric field between two infinitely large parallel conducting plates with surface charge densities $+\sigma$ and $-\sigma$ on their inner surfaces is $E = \frac{\sigma}{\epsilon_0}$. This is derived by superimposing the fields from each plate: $E_1 = \frac{\sigma}{2\epsilon_0}$ (away from positive plate) and $E_2 = \frac{\sigma}{2\epsilon_0}$ (towards negative plate). Both fields add up in the same direction. The force on a point charge +q in this field is $F = qE$. Therefore, $F = q \left(\frac{\sigma}{\epsilon_0}\right)$.