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If we partially introduce a linear, isotropic and homogeneous dielectric slab in a charged, isolated, parallel plate capacitor, we know that it experiences a forces pulling it into the dielectric, and we can obtain the expression of this force using energy considerations. However, when the energy calculation is done, we assume a uniform E field in the capacitor, always perpendicular to the dielectric, so in theory it looks like the E field can't pull on any charge that's in the dielectric to pull it in, yet the energy calculation still reveals a force. Books then say it's the fringing E field outside the capacitor that's pushing the dielectric in, but this fringing field wasn't taken into account when getting the energy!

What's going on? How does this method self correct itself?

Thanks in advance.