- #1
mitleid
- 56
- 1
No numbers here - purely conceptual.
Two thin plates carry total surface charge densities of [tex]\sigma[/tex] and [tex]\sigma_{1}[/tex] respectively. An uncharged conducting slab is placed in between the charged plates, and then outside [tex]\sigma[/tex]. 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 ([tex]\sigma[/tex]) 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 -[tex]\sigma[/tex] and -[tex]\sigma_{1}[/tex].
When it is placed outside the plates the neutral surface will only take on a partial charge from the nearest plate (which is actually [tex]\sigma[/tex]).
But of an odd question that could use some extra commentary.
Two thin plates carry total surface charge densities of [tex]\sigma[/tex] and [tex]\sigma_{1}[/tex] respectively. An uncharged conducting slab is placed in between the charged plates, and then outside [tex]\sigma[/tex]. 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 ([tex]\sigma[/tex]) 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 -[tex]\sigma[/tex] and -[tex]\sigma_{1}[/tex].
When it is placed outside the plates the neutral surface will only take on a partial charge from the nearest plate (which is actually [tex]\sigma[/tex]).
But of an odd question that could use some extra commentary.