How Do Electric Fields Behave in Nested Spherical Charge Distributions?

[leright]

ok, I have an exam on Monday and I know the prof is going to give a problem where we have inner solid sphere of uniform charge density (+), and this sphere is surrounded by an outer spherical shell with a uniform surface charge density (-). He wants us to calculate the e-field "everywhere" with gauss's law, due to this system, meaning the e-field inside the inner solid sphere, the e-field in between the solid sphere and the spherical shell, and finally outside the spherical shell. Obviously, the e-field is going to cancel inside the inner solid sphere. In between the inner solid sphere and the outer shell, the fields due to the solid sphere and the outer shell would add, since in between the solid sphere and the shell they point in the same direction, right? Now, on the outside of the spherical shell it is just going to be the e-field of the spherical shell, right? I just want to know if I am thinking avout this problem right...

Also, if he wants us to find the capacitance by finding the voltage between the two spheres, I can just determine the e-field due to one of the spheres, and then determine the voltage by integrating e-field with respect to r between the distance of the two spheres, right? I am just having lots of trouble thinking through the details if these types of problems, and want to know if my logic is right...these concepts are not 100% clear to me yet..

Also, I'm 90% sure he is going to give us a quadrupole problem, where we have 4 point charges on an axis, each charge a distance 'd' apart. The charge config is a + - + - system, where the charge magnitudes are identical, but just different signs. We need to find the e-field on a point a distance 'a' from the first charge where a >> d, and this point is on the same axis as the 4 charges...I would reason that the e-field due to the individual charges cancel out, since a ~= a + d ~= a + 2d ~= a + 3d, leaving a net e-field at thta point of zero...but this line of reasoning is not good enough for my prof...be wants us to use the binomial theorem. I didn't follow his lecture on this example, and nobody else in the class seemed to either. I asked him about it, but he was still not much help. :( I was hoping you guys have seen this problem betore and you could point me in the right direction.

Also, we haven't discussed magnetic fields yet, but I am aware that e-fields are different from mag-fields. I have the vague understanding that mag-fields are caused by charge current, whereas e-fields are caused by stationary charges that cause potentials on various regions in space...but, my intuitive understanding of magnetism is the same thing...they both cause potentials, but are magnetic fields not due to charges, where e-fields are? If mag-fields are not due to charges, then what are they caused by? So many questions unanswered and it makes my head spin...I am absolutely losts with most of this stuff...it is driving me crazy.

Any help would be greatly appreciated. I will likely add more questions later.

 

[OlderDan]

See the other forum. Please do not double post.

 

[thepatientmental]

Based on the information provided, it seems like you have a good understanding of the concepts and are on the right track with your reasoning for the e-field questions. It is correct that the e-field will cancel inside the inner solid sphere and will add between the solid sphere and the spherical shell since they are pointing in the same direction.

For finding the capacitance, your approach of determining the e-field due to one of the spheres and then integrating it between the two spheres is correct. Just make sure to use the correct formula for capacitance (C = Q/V) and take into account the sign of the charges when calculating the voltage.

Regarding the quadrupole problem, it is important to use the correct formula for the e-field due to a point charge (E = kq/r^2) and take into account the distance between each charge when calculating the net e-field at a point. The binomial theorem may be helpful in simplifying the calculation, but it is not necessary to solve the problem.

As for magnetic fields, they are indeed caused by moving charges, specifically current. They are different from e-fields in that they are vector quantities and can interact with each other. It may be helpful to review the right-hand rule to understand the direction of magnetic fields.

Overall, it seems like you have a good understanding of the concepts and are on the right track. Keep practicing and reviewing the formulas and you should do well on your exam. Good luck!