Charge on a grounded conductor w/ method of images

In summary, the method of images is used to solve for the induced charge on a grounded conductor in the presence of a point charge by creating an image charge that has the same total charge as the actual surface charge. This is because Gauss's law states that the electric field at a given point is determined by the total charge inside, whether it is the actual charge or the image charge.
  • #1
ralqs
99
1
Why is it that whenever the method of images is used to solve for the induced charge on a grounded conductor in the presence of a point charge, the total charge is just the same as the image charge?
 
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  • #3
Gauss's law says that [tex]\oint{\bf E\cdot dA}[/tex] is given by the total charge inside.
This is either the actual surface charge or the image charge, since they give the same E.
 

Related to Charge on a grounded conductor w/ method of images

1. What is a grounded conductor?

A grounded conductor is a material or object that is connected to the Earth through a conducting path. This allows any excess charge on the conductor to flow into the ground and neutralize.

2. How do you determine the charge on a grounded conductor using the method of images?

The method of images is a mathematical technique used to determine the distribution of charges on a grounded conductor. It involves creating a "mirror image" of the original charge distribution across the grounded surface and using the principle of superposition to calculate the total charge.

3. Why is the method of images used specifically for grounded conductors?

The method of images is used for grounded conductors because the grounded surface acts as a boundary condition that simplifies the mathematical calculations. This makes it easier to determine the charge distribution compared to using other methods.

4. Are there any limitations to using the method of images for calculating charge on a grounded conductor?

Yes, the method of images assumes that the grounded conductor is a perfect conductor and that the charge distribution is symmetrical. In reality, these assumptions may not hold true, which can affect the accuracy of the calculations.

5. Can the method of images be used for any shape of grounded conductor?

Yes, the method of images can be used for any shape of grounded conductor as long as the above-mentioned assumptions hold true. However, for complex shapes, the calculations may become more difficult and time-consuming.

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