Calculating Image Line Charges for Multiple Wires

In summary, adding more conductors to a coaxial cable affects the line image charges. I don't know how to calculate the new capacitance.
  • #1
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I have the below figure I took from my textbook from a section that explains how to calculate the capacitance of two transmission wires using image line charges.

line-image-charges.gif


My question is that if I add two more conductors like shown below, how would it affect the line image charges? I'm not sure how to figure out where the image line charges would go, or if this can even be done analytically.

line-image-charges-2.gif
 
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  • #2
We just studied image charges in lecture and I'm trying to understand what you are trying to do. Are those two conductors inside the insulation of a coaxial cable? If so is +q2 connected to 1 and -q2 connected to 2 somewhere at infinity (like the same terminal of a power source)?
 
  • #3
zetadin said:
We just studied image charges in lecture and I'm trying to understand what you are trying to do. Are those two conductors inside the insulation of a coaxial cable? If so is +q2 connected to 1 and -q2 connected to 2 somewhere at infinity (like the same terminal of a power source)?

Conductors 1 and 2 are two conductors on the same voltage source. The other two, -q2 and +q2 on the coax are connected to a separate voltage source. So all four conductors have different potentials. I am trying to calculate the new capacitance of conductors 1 and 2 after adding the coax part, but I just don't know how to go about this. I'm not sure where I would put the line image charges to create the four equipotential surfaces.
 
  • #4
The way I understood it from lecture is that you have to draw the curves from which the charges are supposed to "reflect" along equipotential lines. Then those curves act as "mirrors" in optics.

I think it could be possible to solve this by using Gauss' Law. But I don't have any idea how to accurately get the electric field just outside each of the conductors. If you do manage to get Qenclosed, C=Q/deltaV.

Sorry I can't be of more help.
 
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1. How do I calculate the line charge for multiple wires in an image?

The line charge for multiple wires in an image can be calculated by first determining the total length of each wire. Then, you can use the formula Q = λ * L, where Q is the total charge, λ is the line charge density, and L is the total length of the wires. Finally, you can multiply the calculated total charge by the number of wires in the image to get the total line charge for multiple wires.

2. What is the line charge density and how is it related to the line charge?

The line charge density is the amount of charge per unit length of a wire. It is related to the line charge by the formula λ = Q / L, where λ is the line charge density, Q is the total charge, and L is the total length of the wire. In other words, the line charge density is the charge per unit length that contributes to the total line charge.

3. How does the distance between the wires affect the line charge calculation?

The distance between the wires does not directly affect the line charge calculation. However, it can indirectly impact the total line charge if the wires are not parallel to each other. In this case, the distance between the wires will affect the calculation of the total length of the wires, which is a crucial factor in determining the line charge.

4. Can the line charge for multiple wires be negative?

No, the line charge for multiple wires cannot be negative. The line charge is a measure of the amount of charge present on the wires, and charge is always positive. If a negative value is obtained in the calculation, it is likely due to an error in the input values or the formula used.

5. Is there a specific unit for line charge?

Yes, the unit for line charge is coulombs per meter (C/m). This unit represents the amount of charge per unit length of the wire. Other common units for line charge include coulombs per centimeter (C/cm) and microcoulombs per meter (μC/m).

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