Zayan
- 47
- 4
- Homework Statement
- Calculating flux through a plane cutting two concentric cylinders.
- Relevant Equations
- /integral E.ds = q/e0.
This was asked in an exam. I'll share the photo of the question.
Well firstly as the outer cylinder is grounded, it must have a zero potential. My first doubt is that is it like a capacitor? i.e, will there be any field outside the outer cylinder? If no then how so?
I presumed that it won't have any field lines going out so I only have to calculate the flux through the plane inside the outer cylinder only. Now, since some part of the plane is inside both the cylinders, it must have zero flux as there's no charge enclosed. So I would have to calculate the flux through the two strips which are outside the inner cylinder but inside the outer cylinder. Also the field would be only due to the inner cylinder as the portion is still inside the outer cylinder so no field by the outer one.
Now my second problem is how to calculate the flux. If it were an infinite cylinder I would assume a infinite line charge on the axis of it and simply integrate through the 2 remaining slits slits. But I am unable to do that as I think the stip I'll be choosing would have non uniform field on it so I might have to calculate a double integral which is outside my course.
I've seen some solutions but they do it like it's an infinite cylinder so they just integrate like I mentioned. But I can't seem to figure out if that approach is wrong or not. Also I've seen some solutions calculating the flux with gauss's law, I am doubtful of that too. Can anyone tell me is my reasoning conceptually correct or am I making a conceptual error or maybe missing something.
Well firstly as the outer cylinder is grounded, it must have a zero potential. My first doubt is that is it like a capacitor? i.e, will there be any field outside the outer cylinder? If no then how so?
I presumed that it won't have any field lines going out so I only have to calculate the flux through the plane inside the outer cylinder only. Now, since some part of the plane is inside both the cylinders, it must have zero flux as there's no charge enclosed. So I would have to calculate the flux through the two strips which are outside the inner cylinder but inside the outer cylinder. Also the field would be only due to the inner cylinder as the portion is still inside the outer cylinder so no field by the outer one.
Now my second problem is how to calculate the flux. If it were an infinite cylinder I would assume a infinite line charge on the axis of it and simply integrate through the 2 remaining slits slits. But I am unable to do that as I think the stip I'll be choosing would have non uniform field on it so I might have to calculate a double integral which is outside my course.
I've seen some solutions but they do it like it's an infinite cylinder so they just integrate like I mentioned. But I can't seem to figure out if that approach is wrong or not. Also I've seen some solutions calculating the flux with gauss's law, I am doubtful of that too. Can anyone tell me is my reasoning conceptually correct or am I making a conceptual error or maybe missing something.
Last edited by a moderator: