Electromagnetism: Trouble understanding the D field

[BeBattey]

I've just finished my first term in an undergrad electromagnetism course using Wangsness as a textbook and we ended on the displacement field.

I feel like Wangsness doesn't give a very good explanation of what the whole point of it actually is, and I still don't quite understand how to use it to find the e field inside both a dielectric and a cavity within a dielectric.

If I could get a quick and easy explanation or a point in the right direction I'd greatly appreciate it, thanks!

 

[tiny-tim]

Hi BeBattey!

The electric displacement field (D, measured in coulombs per square metre) is helpful if you know the surface charge distribution (because it's proportional to it).

So if you know the surface charge distribution, that gives you D, and you can immediately find E for different dielectric fillings, provided inserting the dielectric does not alter the surface charge distribution.

So it works eg for a parallel plate capacitor with dielectrics in series (and with edges parallel to the plates), but not for dielectrics in parallel (because the surface charge distribution will change).

 

[BeBattey]

Thanks for the response!

So the surface charge density you're talking about, is that the bound charge mentioned in the textbook? I know the bound surface charge is P dot n-hat, given the polarization of a dielectric, is this what you mean about the proportionality?

 

[tiny-tim]

Hi BeBattey!

I was really thinking about those exam questions where you know the surface charge, either because the question specifically tells you, or because eg it's a sphere and you can use gauss, or it's a capacitor and you know C V and A (area), so you can find σ = Q/A (and D = σñ).

 

[sardar]

Dear student,

Electromagnetism is a complex and fascinating subject, and it is completely normal to have trouble understanding certain concepts, such as the displacement field (D field). The D field is an important concept in electromagnetism as it helps us understand the behavior of electric fields inside dielectric materials and within cavities in dielectric materials.

To put it simply, the D field is a measure of the amount of electric flux passing through a given area. It is related to the electric field (E field) by the equation D = εE, where ε is the permittivity of the material. This means that the D field is directly proportional to the electric field, but it also takes into account the properties of the material it is passing through.

To use the D field to find the E field inside a dielectric or a cavity within a dielectric, you can use the following steps:

1. Determine the permittivity (ε) of the material.
2. Use the equation D = εE to calculate the D field.
3. Use the boundary conditions for electric fields to relate the D field to the E field at the interface between the different materials.
4. Use the D field to calculate the E field inside the dielectric or the cavity.

I would also recommend seeking additional resources, such as online tutorials or practice problems, to help you gain a better understanding of the D field and its applications. Don't be afraid to ask your professor or peers for help as well. With patience and practice, I am confident that you will gain a better understanding of the D field and its role in electromagnetism. Keep up the good work!