Electromagnetism problem

In summary, electromagnetism is the branch of physics that studies the interaction between electrically charged particles and their magnetic fields. An electromagnetic field is a physical field produced by charged objects, responsible for exerting forces between them. The main difference between an electric and magnetic field is their origin and the direction of the forces they exert on charged particles. Electromagnetism has numerous everyday applications, from electronic devices to power generation, transportation, and medical imaging. The study of electromagnetism has also contributed to scientific advancements, including the development of electricity and magnetism as separate fields, the understanding of their relationship, and the discovery of electromagnetic waves, leading to the development of communication technologies.
  • #1
sachi
75
1
We have two hollow concentric conducting spheres which are intially isolated from their surroundings and each other. they are connected electrically, and the outer is connected to a potential source V, the connection between the spheres is then broken. finally the outer sphere is connected to earth. determine the final charge and potential of the inner sphere.

I think the solution is as follows: when the two spheres are connected electrically they are at the same potential V. since the two spheres are at the same potential, there should be no difference is charge on them due to Q=CV, where Q is the charge displaced between the capacitor plates (n.b I think this means that both spheres have no charge, but could it mean that they have equal charge?) Assuming for the moment that they both have no charge, then when the connection is broken, the inner sphere remains with no charge but potential V. the outer sphere is connected to Earth and therefore has no charge or potential. I'm made a little uneasy by this solution, as it shows that there is no difference in charge between the two spheres, and yet there is a potential difference between them (doesn't this violate Q=CV?). Is it possible for charge to be induced from Earth to the outer sphere? thanks for your help.

Sachi
 
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  • #2
, thank you for your post. Your solution is partially correct, but there are a few key points that need to be clarified.

First, when the two spheres are connected electrically, they are indeed at the same potential V. However, this does not necessarily mean that they have no charge. In fact, it is likely that they will have equal and opposite charges due to the potential difference between them. This is because the charge on a conductor is distributed in such a way that the potential is the same everywhere on its surface.

Therefore, when the connection is broken, the outer sphere will still have a charge Q (equal in magnitude but opposite in sign to the charge on the inner sphere) and a potential V. The inner sphere will also have a charge -Q and a potential V, as you correctly stated.

Now, when the outer sphere is connected to Earth, it will lose its charge and its potential will drop to 0. However, this does not mean that the potential of the inner sphere will also drop to 0. This is because the inner sphere is still isolated from its surroundings and has a charge Q. As a result, it will have a potential V, which is the same potential it had when it was connected to the outer sphere before it was connected to Earth.

In summary, the final charge on the inner sphere will be -Q and its final potential will be V. The key point to remember is that the charge on a conductor can redistribute itself, but the potential of the conductor will remain the same as long as it is isolated from its surroundings.

Regarding your question about charge being induced from Earth to the outer sphere, it is possible for a small amount of charge to be induced on the outer sphere due to the potential difference between the two spheres. However, this charge will be very small and will not significantly affect the potential of the outer sphere.

I hope this helps clarify any confusion. Please let me know if you have any further questions.
 

1. What is electromagnetism?

Electromagnetism is the branch of physics that deals with the study of the interaction between electrically charged particles and their magnetic fields.

2. What is an electromagnetic field?

An electromagnetic field is a physical field that is produced by electrically charged objects and is responsible for the forces exerted between those objects.

3. What is the difference between an electric field and a magnetic field?

An electric field is produced by stationary electric charges, while a magnetic field is produced by moving electric charges or permanent magnets. Additionally, electric fields exert forces on charged particles in the direction of the field, while magnetic fields exert forces perpendicular to the direction of the field.

4. How is electromagnetism used in everyday life?

Electromagnetism is used in numerous everyday devices such as televisions, computers, and cell phones. It is also used in power generation, transportation, and medical imaging.

5. How does the study of electromagnetism contribute to scientific advancements?

The study of electromagnetism has led to numerous scientific advancements, including the development of electricity and magnetism as separate fields, the understanding of how electricity and magnetism are related, and the discovery of electromagnetic waves which led to the development of various communication technologies.

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