# Do you think this makes sense?

• LucasGB
In summary, when a spherical gaussian surface is very close to the surface of a charged sphere, but not at the surface of the sphere, the electric field is Q/(epsilon 0 times area of the surface), where Q is the charge of the sphere. However, when the gaussian surface is at the surface of the sphere, there is a discontinuity in the electric field, with half the charge being inside the surface and half outside. This results in a field of Q/2(epsilon 0 times area of the surface), which is half the electric field at extreme proximity. Inside the sphere, the field is zero. The definition of the surface of the sphere can affect the presence of this discontinuity.
LucasGB
When a spherical gaussian surface is very close to the surface of a charged sphere, but not at the surface of the sphere, the electric field is, according to Gauss' Law:

Q/(epsilon 0 times area of the surface)

where Q is the charge of the sphere. But when the gaussian surface is at the surface of the sphere, half the charge is inside the surface, and half the charge is outside. (Think of a line of atoms with orbiting electrons. The gaussian surface is leveled with the nuclei, so statistically speaking, half the electrons are above it, and half are below it.) Therefore, according to Gauss' Law, the electric field is:

Q/2(epsilon 0 times area of the surface)

Which is half the electric field at extreme proximity. Inside the sphere the field would, of course, be zero. Does this seem sensible to you?

I guess it just depends on what you define to be the surface of the sphere.

If I define the surface of the sphere as the level I mentioned (leveled with the nuclei of the atoms of the outermost layer) then we can say there is a discontinuity in the electric field? Outside the sphere it falls with the inverse square, inside the sphere it is zero, and at the surface it is half the field at extreme proximity. Is this right?

LucasGB said:
If I define the surface of the sphere as the level I mentioned (leveled with the nuclei of the atoms of the outermost layer) then we can say there is a discontinuity in the electric field? Outside the sphere it falls with the inverse square, inside the sphere it is zero, and at the surface it is half the field at extreme proximity. Is this right?
No, since "at the surface" is not clearly defined.

Whenever you apply Gauss's law to a charged surface you'll get a discontinuity in the electric field. (Note that the charge is always contained within the Gaussian surface and not on it.) Consider an infinite plane sheet of charge. The field on one side is +σ/2ε0 and the other it is -σ/2ε0.

If that bothers you, then instead of arbitrarily modeling the surface charge on the sphere as being two surfaces, picture it as a uniform band of charge. That way you can imagine the field smoothly varying from zero to its full value outside of the sphere.

## 1. What does "makes sense" mean in this context?

When someone asks if something "makes sense," they are generally asking if it is logical, reasonable, or understandable. In a scientific context, this could refer to a hypothesis, experiment, or theory being supported by evidence and following the principles of scientific reasoning.

## 2. Why is it important for things to "make sense" in science?

In science, making sense means that the information and conclusions presented are accurate and supported by evidence. This is important because it ensures that scientific findings are reliable and can be replicated by others, leading to a better understanding of the natural world.

## 3. Can something still be valid if it doesn't "make sense"?

In science, validity refers to the accuracy and soundness of an experiment or study. If something does not make sense, it is likely not valid as it may not be supported by evidence or follow the principles of scientific reasoning. However, there may be instances where further research and evidence can change our understanding and what makes sense.

## 4. How can we determine if something "makes sense" in science?

In science, we use the scientific method to determine if something makes sense. This involves forming a hypothesis, conducting experiments to test it, analyzing the results, and drawing conclusions based on the evidence. If the evidence supports the hypothesis and it follows the principles of scientific reasoning, then it can be considered to make sense.

## 5. Is "making sense" subjective in science?

While there may be some subjectivity in interpreting evidence and drawing conclusions, the overall goal of science is to be objective and unbiased. This means that the evidence and reasoning used to determine if something makes sense should be based on facts and not personal beliefs or opinions. Therefore, while there may be some subjectivity, the scientific community strives to minimize it and reach a consensus on what makes sense based on the available evidence.

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