Faraday's Nested Sphere Experiment

In summary, the Faraday's Nested Sphere Experiment involves analyzing the electric field equations and the charge distribution on the outer spherical shell. Gauss's law is used to determine the flux density, which is radially outward for both the outer and inner surface. The field inside the outer conductor can be neutralized by placing a charge of -Q on the inner surface. However, in a situation where the outer sphere is grounded, the charge distribution on the outer surface must be 0, resulting in a total charge of +Q on the outer surface. This leads to a higher electric field at a specific point, compared to a situation where the outer sphere is not grounded. Ultimately, the analysis of this experiment should be done using the electrostatic Maxwell equations
  • #1
BlackMelon
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Hi there!

I have a question about the Faraday's Nested Sphere Experiment, please see the attached pdf. I wonder why equation (1) and the electric field's equation ( coming after (1) ) consider only the charge Q. Why there aren't charge -Q in the equation?

Ps. I'm thinking about point charges. When you have two charges: +Q and -Q, and you want to find the electric field at point x. You need to put both +Q and -Q in an equation:
1681479342482.png


BlackMelon
 

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  • #2
Because the flux density is radially outward for both (via Gauss's law) . For the outer shell this is into the local surface of the outer shell.
It is true that there needs to be -Q on the inside of the outer shell to kill the field inside the outer conductor. Thus +Q is left on the outside of the outer conductor before it is grounded.
 
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  • #3
About the Gauss's law, could you take a look at the file inside the link below?

SITUATION 1:
There were positive charges at the outer surface of the outer shell. As we connect the ground, the outer surface becomes neutral.
Afterwards, I define the gaussian surface (dotted line). The magnitude of electric field at each point normal to the gaussian surface is E1.

SITUATION2:
This experiment has only the same charge +Q and the same gaussian surface. No other instruments.
The magnitude of electric field is E2.

Is E1 > E2?
From the bottom most picture, I inspect the two negative charges (blue one and green one) and their effects on the Gaussian surface (red circle). At x, the blue one will add up with the field from the positive charge. The green one will deduct the field, but its effect is lesser, since it is far away from x. So in total, the field coming out of x will be more than that in the situation 2. Am I correct?

BlackMelon

The attached picture resolution is not good. Take this link:
https://www.mediafire.com/file/npoqe0qaekziezs/Gaussian1.jpg/file
 
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  • #4
I don't know, if it is so helpful to use such hand-waving arguments. Rather one should analyze the problem, using the electrostatic Maxwell equations. Since the problem is spherically symmetric, it's clear that the em. field everywhere has the form of a Coulomb field
$$\vec{E}=\frac{q}{4 \pi \epsilon_0 r^3} \vec{r}.$$
For the grounded outer sphere you have the outer surface at equal potential ##0##, and thus outside the outer surface the field is ##0##. This implies that at the inner surface of the outer spherical shell must be a total charge ##-Q##.

If you have the situation before grounding the outer sphere, then the total charge on both its inner and outer surface must be 0, because it was 0 before putting it around the inner sphere, and no net-charge has been in any way transported from or to the outer sphere. This is achieved by simply putting a total charge ##+Q## on the outer surface of the outer shell compared to the situation when the outer sphere is grounded. Thus in this case you have outside again the Coulomb field with ##q=+Q##.
 
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Related to Faraday's Nested Sphere Experiment

What is Faraday's Nested Sphere Experiment?

Faraday's Nested Sphere Experiment, also known as Faraday's Ice Pail Experiment, is a classic demonstration of electrostatic principles. It involves placing a charged object inside a conductive container (often a metal sphere) and observing the distribution of electric charge. The experiment illustrates that the electric field inside a conductor is zero and that charges reside on the outer surface of the conductor.

Why is Faraday's Nested Sphere Experiment important?

This experiment is important because it provides empirical evidence for several key principles of electrostatics, such as Gauss's Law and the behavior of conductors in electrostatic equilibrium. It demonstrates that the electric field inside a closed conductor is zero, which has implications for shielding sensitive equipment from external electric fields (Faraday Cage effect).

How does Faraday's Nested Sphere Experiment demonstrate charge distribution?

When a charged object is introduced inside the inner sphere without touching it, the charges on the object induce an equal and opposite charge on the inner surface of the sphere. This causes the same amount of charge to appear on the outer surface of the sphere. The experiment shows that the induced charge on the inner surface cancels the electric field inside the conductor, resulting in zero electric field within the conducting material itself.

What materials are needed to perform Faraday's Nested Sphere Experiment?

The basic materials required for the experiment include a conductive container (such as a metal sphere or pail), a charged object (like a metal ball), an electroscope to detect charge, and insulating materials to prevent unwanted charge transfer. Additional equipment like a stand or support for the spheres and a method to charge the object (e.g., a Van de Graaff generator) may also be used.

Can Faraday's Nested Sphere Experiment be used to explain the Faraday Cage effect?

Yes, Faraday's Nested Sphere Experiment provides a fundamental understanding of the Faraday Cage effect. It demonstrates that the electric field inside a closed conductor is zero because the charges redistribute themselves on the outer surface of the conductor. This principle is applied in Faraday Cages to shield sensitive electronic equipment from external electric fields and electromagnetic radiation.

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