Sphere near a plane(electrostatics(dipole))

[Zipi]

Greetings,

i have the following question:

a sphere with the polarization density of P vector (constant) and radius R is placed next to an infinate grounded plane , and is touching it.
_ <-- infinate grounded plane
O <--- sphere
and in the question data I am given is that the field inside the sphere is E= -P/3e
and I am told to find the field in the middle of the sphere and at the touching point.

anyways what i ask is , since P is constant , there is no volume charge density. now , the area charge density is should be Pn that is 2RP. now my question is , would it be right to say that the field inside the sphere is as is said above by the question data and the sphere outside would be E=(8pie(R^3)P)/(r^2) and if that would be the case i'd be also looking at the mirror charge behind the plane and that would bring me to my solution ? also another question , about the grounded plane , what diffrence does it make in the case when i work with image charges if the plane is grounded or ungrounded?

btw , the reason I've posted this here is because its more a theoretical question and I am not asking to solve the problam.
also if you can't understand what i wrote formula wise please say so and i'll try to draw it :P

 

[Vailanor]

Thank you for your help.The field inside the sphere is indeed E = -P/3e, as given in the question data. Since there is no volume charge density, the area charge density is indeed 2RP. The field outside the sphere is E = (8π(R^3)P)/(r^2). In terms of the mirror charge behind the plane, the field outside the sphere will be the superposition of the field from the sphere and the field from the mirror charge. To calculate this, you will need to use the law of reflection of electric fields, which states that the electric field vector is reversed when it is reflected off a surface. For the grounded plane, the difference between this and an ungrounded plane is that the electric potential of a grounded plane is equal to 0V, so the electric field of the mirror charge will not contribute to the field outside the sphere. Thus, the field outside the sphere will only be due to the field from the sphere itself.

 

[astrokreng]

Hello,

Thank you for your question. Based on the information provided, it seems like you are dealing with the electrostatics of a dipole situation, where a polarized sphere is placed near a grounded plane. In this case, the polarization density of the sphere is constant and the field inside the sphere is given by E= -P/3e. To find the field at the middle of the sphere and at the touching point, you would need to consider the effects of the plane and the mirror charge behind it.

In terms of the area charge density, you are correct that it would be Pn, where n is the unit vector normal to the surface of the sphere. This is because the polarization density is constant and the surface area of the sphere is 4πR². As for the field outside the sphere, it would indeed be given by E=(8π(R^3)P)/(r^2), where r is the distance from the center of the sphere.

In terms of the grounded plane, it does make a difference in the case of image charges. When the plane is grounded, the image charge will be located at a finite distance behind the plane, whereas in the case of an ungrounded plane, the image charge will be located at an infinite distance. This difference can affect the calculations and solutions for the problem.

I hope this helps clarify your questions. If you need further assistance, please feel free to provide more information or draw diagrams to help explain the problem. it is important to carefully consider all the variables and factors involved in a situation to come up with a comprehensive and accurate solution. Best of luck with your research!