Question

Force between two conducting large plates with charges q and q/2 area of each face of page is a

Answer 1

Given:

Two conducting large plates have charge q and q/2 respectively. Each have area of "a" units.

To find:

Force between the plates.

Calculation:

The general formula for electrostatic field intensity for a large conducting plate is:

$\boxed{ \sf{E = \dfrac{ \sigma}{ 2\epsilon_{0} } }}$

Now, Electrostatic field Intensity of the plate A in the region of plate B will be :

$\sf{E = \dfrac{ \sigma}{ 2\epsilon_{0} } = \dfrac{q}{2a\epsilon_{0}} }$

Now, force experienced by plate B will be :

$\boxed{ \sf{force = \dfrac{q}{2} \times E = \dfrac{ {q}^{2} }{2a\epsilon_{0}} }}$

Similarly, force experienced by Plate A will be:

$\sf{force = q\times( E2) }$

$\sf{ = > force = q\times( \dfrac{ \frac{q}{2} }{2a \epsilon_{0}} ) }$

$\boxed { \sf{ = > force = \dfrac{ {q}^{2} }{4a \epsilon_{0}} }}$