Calculating the Electric Field outside a dielectric

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In the textbook (Introduction to Electrodynamics by Griffiths), the problem in the attached image asks to find the electric field ##E## outside a dielectric. The problem consists of dividing the electric field into the one produced by the negative charges in the dielectric and another by the positive charges and adding them up.
However, what I don't understand is that since for the polarization to be there, there needs to be an external Electric field that caused it in the first place, which would have to be included in the calculation, but clearly wasn't. What's the reason behind this?

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However, what I don't understand is that since for the polarization to be there, there needs to be an external Electric field that caused it in the first place,
Not necessarily. That would be true for a linear dielectric, but there are many nonlinear dielectrics. Some of these can exhibit considerable hysteresis and maintain polarization after the polarizing field is removed.
 
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The same is true for problems in magnetostatics. It is a very good approach to learn how to calculate the resulting electric or magnetic fields that occur for the case of spontaneous polarization or magnetization that stays at some fixed value, before trying to do the more difficult problem of an applied field to which the material responds. ## \\ ## In this latter case, it turns out to be a self-consistent problem because the resulting polarization or magnetization can generate its own field that adds/subtracts from the applied field. The material often responds in a linear fashion to the total field at a given location. See also: https://www.physicsforums.com/threa...harged-dielectric-sphere.890319/#post-5601535 ## \\ ## In addition, the magnetic field from a cylindrical permanent magnet can be analyzed by considering it to be a case of uniform magnetization ##\vec{M }##, which is a very good approximation in many cases. There are no external magnetic fields required for the permanent magnet to remain magnetized.
 
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