Calculating the electric field

[america8371]

Hi everyone,
I have just finished reading the chapter in my book where it discusses the electric field, electric flux, Coulomb's law, Gauss's law, etc. I think my biggest problem is knowing which to equations to use and how to relate them to models that aren't int the examples. Like the book gives an example on the electric field due to an infinite line charge which will seems simple enough using the equation that I'm provided. But when the professor will give me a question about an infinitely long cylinder which wasn't one of the examples then it just throws me off. Or the book give me an example of finding the electric field due to a charged spherical shell. Then the professor will give me a question on the electric field due to a point charge and a charged spherical shell. I know there is a method to knowing which equations to use and how to go about the problem, but I'm just having so much trouble grasping the concept.

 

[ZapperZ]

Hi everyone,
I have just finished reading the chapter in my book where it discusses the electric field, electric flux, Coulomb's law, Gauss's law, etc. I think my biggest problem is knowing which to equations to use and how to relate them to models that aren't int the examples. Like the book gives an example on the electric field due to an infinite line charge which will seems simple enough using the equation that I'm provided. But when the professor will give me a question about an infinitely long cylinder which wasn't one of the examples then it just throws me off. Or the book give me an example of finding the electric field due to a charged spherical shell. Then the professor will give me a question on the electric field due to a point charge and a charged spherical shell. I know there is a method to knowing which equations to use and how to go about the problem, but I'm just having so much trouble grasping the concept.

Coulomb's law always work in any charge configuration and geometry. The problem here is that in cases where there is high symmetry, Gauss's Law may be simpler.

What does "high symmetry" means? It means that you can construct a simple Gaussian surface in which the electric field crossing that surface is either a constant and/or zero. This means that you have to have an idea of what the E-field looks like for a given charge distribution. Let's do a few examples:

1. A spherically symmetry charge. Here, with the origin at the center of the sphere, you can construct a spherical Gaussian sphere where the E-field crossing all points on the surface of the sphere is a constant.

2. An infinite line charge. Here, you can construct a cylindrical gaussian sphere of a certain length, say L, around the line charge. What you will see is that on the curved surface of the sphere, the E-field is a constant everywhere, while on the 2 round ends, the E-field is zero everywhere.

3. Infinite plane of charge. Here, you can construct a "pillbox" shaped gaussian surface that is imbeded into the surface. This time, the curved surface has zero E-field everywhere, while the round flat surface has constant E-field everywhere.

Without those highly symmetry situation, it is extremely difficult to effectively use Gauss's Law to calculate E-field. One can still make use of it in qualitative situation under non-highly symmetry cases, such as "proving" why there are no E-field in a conductor under electrostatic situation or why charges only reside on the surface of a conductor under the same situation, but one cannot come up easily with quantitative answers.

Zz.

 

[america8371]

Coulomb's law always work in any charge configuration and geometry. The problem here is that in cases where there is high symmetry, Gauss's Law may be simpler.

What does "high symmetry" means? It means that you can construct a simple Gaussian surface in which the electric field crossing that surface is either a constant and/or zero. This means that you have to have an idea of what the E-field looks like for a given charge distribution. Let's do a few examples:

1. A spherically symmetry charge. Here, with the origin at the center of the sphere, you can construct a spherical Gaussian sphere where the E-field crossing all points on the surface of the sphere is a constant.

2. An infinite line charge. Here, you can construct a cylindrical gaussian sphere of a certain length, say L, around the line charge. What you will see is that on the curved surface of the sphere, the E-field is a constant everywhere, while on the 2 round ends, the E-field is zero everywhere.

3. Infinite plane of charge. Here, you can construct a "pillbox" shaped gaussian surface that is imbeded into the surface. This time, the curved surface has zero E-field everywhere, while the round flat surface has constant E-field everywhere.

Without those highly symmetry situation, it is extremely difficult to effectively use Gauss's Law to calculate E-field. One can still make use of it in qualitative situation under non-highly symmetry cases, such as "proving" why there are no E-field in a conductor under electrostatic situation or why charges only reside on the surface of a conductor under the same situation, but one cannot come up easily with quantitative answers.

Zz.

Thanks ZapperZ, that actually helped me a bit. But I didn't quite catch #2.