Charged plane in an electric field acceleration

Question

A perpendicular plane to an electric field's lines of force has more electric flux than a plane that is in parallel with the lines of force, right?

Does this mean that a charged plate would experience less acceleration if parallel to rather than perpendicular to the lines of force?

EDIT

Another example of this question would be a charged object inside a charged sphere... would any force act upon it?

Answer 1

Velox,

Let's assume the following for conceptual simplicity:

1. The plate is an insulator with uniform surface charge density $\sigma$.

2. The electric field $\mathbf E(\mathbf x)$ is uniform, so there exists some vector $\mathbf E_0$ for which $\mathbf E(\mathbf x) = \mathbf E_0$ for all $\mathbf x$.

In both cases, the force on the plate $P$ is given by $$ \mathbf F = \int_P dA \sigma \, \mathbf E(\mathbf x) $$ where $dA$ is a surface area element on the plate. Since the electric field was assumed constant, it comes out of the integral, and the remaining integral just gives the total charge $Q$ on the plate, so we get $$ \mathbf F = Q\mathbf E_0 $$ The result is the same in both cases! However, if the electric field were not uniform, or if the charge density on the plate were not uniform, then in general the results would have been different.

Hope that helps!

Cheers!