Finding E and V involving 2 planes.

[xxbigelxx]

Great. Do I leave them as distinct quantities, or can I combine them? The questions says "Determine V for all points" so I feel like there should be another form of the answer.

 

[kuruman]

The way to present the solution is by listing the potentials in each region, such as

V(x,y,z) = ... for x ≥ 6 cm (top region)
V(x,y,z) = ... for 6 cm ≥ x ≥ -4 cm (in-between region)
V(x,y,z) = ... for x ≤ -4 cm (bottom region)

 

[xxbigelxx]

Ok I see what you are saying. I think you meant to say z instead of x for all those bounds you gave, but I agree otherwise. And all of those units should be 'V' I believe as well.

Finally for the drawing of the equipotentials, they are just going to be planes parallel to the z planes right?

 

[noface]

Yeah, they're just planes with normal vector in the z direction. I'm confused about the middle region...why wouldn't the "-4" be involved at all in the bounds. I have the same thing for the other two regions and understand why, but I don't understand why the middle region wouldn't be limited by the physical boundary of -4.

 

[kuruman]

Ok I see what you are saying. I think you meant to say z instead of x for all those bounds you gave, but I agree otherwise. And all of those units should be 'V' I believe as well.

Sorry, yes I meant to say z instead of x for all the bounds.

 

[xxbigelxx]

I can't answer for sure, but I would guess it's just because you are only interested in the plate where the E is originating (in this case at z= 6cm)

 

[Mindscrape]

Yeah, they're just planes with normal vector in the z direction. I'm confused about the middle region...why wouldn't the "-4" be involved at all in the bounds. I have the same thing for the other two regions and understand why, but I don't understand why the middle region wouldn't be limited by the physical boundary of -4.

Because -4 isn't the reference point. If you wanted the capacitance then you would need the potential difference between V(6) and V(-4), otherwise it doesn't matter. Don't worry, the boundaries solve any issues of ambiguity.

Lastly, don't worry, this is a textbook problem. It's meant for you to learn about EM. In reality, with no approximations, you would always set the reference voltage at infinity. Griffiths has a good discussion of this.