Radial field due to ring

What and also how to easily derive the radial field due to a ring of radius R at a distance r from the axis of ring, (r<<R)? (slightly outside the ring)
21 Replies
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@Gyro Gearloose
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Opt
Opt2mo ago
Inside the ring? You need to take approximations. Wait i had this
SirLancelotDuLac
SirLancelotDuLacOP2mo ago
Oh sorry. Slightly Outside Wait I think I should share the whole question first.
Opt
Opt2mo ago
Yes
SirLancelotDuLac
SirLancelotDuLacOP2mo ago
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SirLancelotDuLac
SirLancelotDuLacOP2mo ago
Yep. This is the question. ⬆️
Opt
Opt2mo ago
Ok, I think I understood So basically the field at a point slightly displaced from the axis? And close to the ring
Opt
Opt2mo ago
Am I right?
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SirLancelotDuLac
SirLancelotDuLacOP2mo ago
Ye exactly this situation
Opt
Opt2mo ago
I'm not getting a simple answer for this :sweaty: I couldn't find the apt symmetry condition, so I tried the integral form And while it's integrable, let's just say it looks very messed up Let me have breakfast What's the best Gaussian surface aaaaaaaa No way, is it zero? @SirLancelotDuLac Never mind flux cancels out
SirLancelotDuLac
SirLancelotDuLacOP2mo ago
Ye that is one of the roadblocks I'm having. No charge gets enclosed in choosing a surface and flux gets cancelled out
Opt
Opt2mo ago
Imagine it's a weird Gaussian surface like a torus enclosing the ring
SirLancelotDuLac
SirLancelotDuLacOP2mo ago
It shouldn't be anything cylindrically symmetric with the circle no? So as to not let the flux be cancelled ig?
Opt
Opt2mo ago
It won't be cancelled if the ring is inside. You have non-zero flux Everything is outwards. Looking at the options, there is no dependence on distance from the plane
SirLancelotDuLac
SirLancelotDuLacOP2mo ago
Doesn't the radial flux pushing the stuff inside (the portion below a cylinder enclosing the ring itself) compensates the low area with E-field? Oh no wait Im dumb. Can you send the full solution once please? Also, is it safe to assume the radial component doesn't depend on the distance from the ring?
Opt
Opt2mo ago
I'm eating rn. Just contemplating That's my comcern It's clearly going to depend because inverse square But for small d, it must be an approximation @SirLancelotDuLac is it option 2? I did a stupid approximation and got 2
SirLancelotDuLac
SirLancelotDuLacOP2mo ago
It's (1) according to the answer key.
Opt
Opt2mo ago
Screw it I'm gonna try integrating And of course that doesn't work It's just too tedious @SirLancelotDuLac did you try finding field for a point in the plane?
SirLancelotDuLac
SirLancelotDuLacOP2mo ago
I tbh did not want to assume independancy from d so can't say I have. But that would be constructive tp the problem yeah. Apart from the point on the circumference, how would you find the radial field at a point inside the ring? Ah dude, life hits harder when you realize the question tells you how to do it and yet you skip the paragraph. :sweaty: +solved @Opt
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