- #1
askcr9
- 10
- 2
- Homework Statement
- Consider a slab centered at the origin with uniform volume charge density, ρ. The slab is infinitely long in the y-z plane, but has thickness d along the x axis. Calculate the magnitude of the electric field due to the slab
i. outside (x > d/2,) and
ii. inside (0 < x < d/2).
[see attachment for figure]
- Relevant Equations
- Well, it's electric field, so I'm assuming Gauss' Law is the best way to solve this thing… and… I think that's the only formula you need.
So, yeah, Gauss' Law is the integral of E dot dA equals charge enclosed divided by permittivity of free space… yeah, you know the whole deal… the equation is in the first line of my work which is attached.
The first time I saw this question I had no idea how to do it (as you can see in the figure, I lost a lot of points :s) because I was confused on how to even approach it with area of the slab from all sides being infinity. Right? That's problematic, no?
Today, I just tried the problem again for the first time in a while and I got an answer but I don't know if it's correct. (Well, I got an answer for part i; I haven't done part ii yet, but once I find out how to do part i, I know doing part ii will be real easy. Mathematically, it'll be, like, the same exact thing as part i with just a different value of charge enclosed. But anyway, yeah, the point is, I've only done part i so far.) See attachment for my work; the answer I got was ρ/xϵ0. I'm guessing this isn't correct, cause area canceled out when I was solving for it so it's independent of area… and how could the electric field generated by this thing be independent of its area? That doesn't make any sense… right?
Like, the electric field generated by this infinite slab would have to be different from the electric field generated by a finite slab, right? My answer goes against that notion.
Any help would be appreciated. Thank you!
Today, I just tried the problem again for the first time in a while and I got an answer but I don't know if it's correct. (Well, I got an answer for part i; I haven't done part ii yet, but once I find out how to do part i, I know doing part ii will be real easy. Mathematically, it'll be, like, the same exact thing as part i with just a different value of charge enclosed. But anyway, yeah, the point is, I've only done part i so far.) See attachment for my work; the answer I got was ρ/xϵ0. I'm guessing this isn't correct, cause area canceled out when I was solving for it so it's independent of area… and how could the electric field generated by this thing be independent of its area? That doesn't make any sense… right?
Like, the electric field generated by this infinite slab would have to be different from the electric field generated by a finite slab, right? My answer goes against that notion.
Any help would be appreciated. Thank you!