Three concentric conductors, one grounded (Potential)

In summary, the conversation discusses how to calculate voltage between two points using the path integral of the electric field. The confusion arises regarding the chosen path and how the electric field can be integrated over it to determine the voltage. However, it is explained that in electro-static problems, the electric field is a conservative field, making the integrals path independent. This is proven in many elementary E&M texts and is how voltage between two points is defined.
  • #1
jegues
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3

Homework Statement



See figure attached.

Homework Equations





The Attempt at a Solution



See figure attached.

I'm confused how they deduced that V1-V2 is going to be the integral of the electric field from a to b.

How do they choose the path from a to b?

How can they say that the electric field integrated over this path is going to be V1-V2?

I express the same confusion over the 2nd integral, why is V2 equal to the electric field integrated from c to d?
 

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  • #2
The path doesn't matter. Since this is an electro-static problem, the E field is a conservative field, meaning that integrals are path independent. You can find a proof of this in most elementary E&M texts. The voltage between two points is the path integral of E between those two points, that is how it is defined.
 

1. What is the purpose of using three concentric conductors with one grounded?

The three concentric conductors with one grounded are used for high voltage power transmission. The grounded conductor acts as a shield for the other two conductors, reducing the risk of electrical interference and increasing safety.

2. How does the grounding of one conductor affect the potential of the other two conductors?

The grounded conductor acts as a reference point for the other two conductors, maintaining their potential difference. This allows for the safe transmission of high voltages without any significant loss of energy.

3. What type of material is used for the three concentric conductors?

The three concentric conductors are typically made of different layers of aluminum or copper. These materials have high conductivity and are able to withstand the high voltages used in power transmission.

4. How is the grounding of the conductor achieved?

The grounding of the conductor is achieved by physically connecting it to the ground using metal rods or plates. This creates a low resistance path for any excess electrical energy to dissipate, protecting the other conductors and equipment.

5. Are there any disadvantages to using three concentric conductors with one grounded?

One potential disadvantage is the increased cost of using three conductors instead of just two. There may also be technical challenges in maintaining the balance of the three conductors to ensure efficient power transmission. Additionally, the grounding of the conductor may increase the risk of corrosion and require regular maintenance.

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