Induced charge between/above infinite charged plates

[mitleid]

No numbers here - purely conceptual.

Two thin plates carry total surface charge densities of $$\sigma$$ and $$\sigma_{1}$$ respectively. An uncharged conducting slab is placed in between the charged plates, and then outside $$\sigma$$. What are the induced charged densities on the surfaces of the conducting slab in each of the configurations?

The problem also states that 'polarities of those charges ($$\sigma$$) are not specified and should be treated algebraically'.

Every example I can find using infinite parallel plates has to do with opposite charged densities. However, this problem does not denote opposite charges of the plates, so... I'm assuming the algebraic note above solves this issue.

For the first configuration (in between), since each of these plates is charged it will induce the opposite charge on the conductive surface in order to create a potential flow (though that part isn't important in this question). So my first guess is the charge densities on the -neutral- surface will become -$$\sigma$$ and -$$\sigma_{1}$$.

When it is placed outside the plates the neutral surface will only take on a partial charge from the nearest plate (which is actually $$\sigma$$).

But of an odd question that could use some extra commentary.

 

[mitleid]

Ah, so... apparently I'm not sure how to treat the polarities algebraically... which is key here I think.

 

[m2003]

I would approach this problem by first clarifying the given information and assumptions. The problem states that the plates carry total surface charge densities of \sigma and \sigma_{1}, but does not specify the polarity of these charges. Therefore, I would assume that both plates have the same polarity and treat them algebraically as \pm\sigma and \pm\sigma_{1}.

In the first configuration, the conducting slab is placed in between the charged plates. This will result in induced charges on the surfaces of the slab in order to maintain the electric field equilibrium between the plates. Since the plates have opposite charges, the induced charges on the conductive surface will also be opposite, resulting in -\sigma and -\sigma_{1}.

In the second configuration, the conducting slab is placed outside the plates. In this case, the neutral surface will only experience a partial charge from the nearest plate, which is \sigma. This is because the electric field from the other plate is cancelled out by the conducting slab. Therefore, the induced charge on the surface of the slab will be -\sigma.

It is worth noting that this problem assumes an idealized scenario with infinite parallel plates, which is not possible in reality. In a real-world situation, the induced charges may also depend on the distance between the plates and the conducting slab, as well as the shape and material properties of the plates and the slab.

Overall, the concept of induced charges between and above infinite charged plates is important in understanding the behavior of electric fields and how they interact with conductive materials. It is a fundamental concept in electromagnetism and has many practical applications in various fields of science and technology.