Calculating the Electric Field outside a dielectric

In summary, 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 is unclear is why this needs to be done in the first place, when the resulting field can be obtained by multiplying the two fields together. Additionally, 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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bubblewrap
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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?

Thanks.
 

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bubblewrap said:
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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Related to Calculating the Electric Field outside a dielectric

1. How do you calculate the electric field outside a dielectric?

To calculate the electric field outside a dielectric, you can use the equation E = (1/4πε0)(Q/r2), where Q is the charge of the object creating the field, r is the distance from the object, and ε0 is the permittivity of free space.

2. What is a dielectric material and how does it affect the electric field?

A dielectric material is an insulating material that can be polarized by an electric field. This polarization causes the material to have a different permittivity, which affects the strength of the electric field in the surrounding space.

3. Can the electric field outside a dielectric be zero?

Yes, the electric field outside a dielectric can be zero if the dielectric material is placed between two parallel conducting plates with opposite charges. In this case, the electric field inside the dielectric cancels out the electric field outside.

4. How does the shape of the dielectric affect the electric field outside?

The shape of the dielectric can affect the electric field outside by changing the distribution of charges. For example, a spherical dielectric will have a different electric field compared to a cylindrical dielectric with the same charge and distance from the source.

5. What is the relationship between the permittivity of a material and the electric field outside a dielectric?

The permittivity of a material is directly proportional to the strength of the electric field outside a dielectric. A higher permittivity means that the material can be polarized more easily, resulting in a stronger electric field outside the dielectric.

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