Electric field due to a charged ring off-axis

In summary, the conversation discusses the process for finding the electric field due to a charged ring off-axis, specifically for two ring electrodes in parallel. The steps involve finding phi on the axis, expanding it in a Taylor series, using the expansion to write the Legendre polynomial expansion for all angles, and taking the gradient of phi to obtain the electric field. While the process is more complicated for two rings, it is still possible to find the electric field. This topic is typically covered in advanced electromagnetic texts.
  • #1
a789irfan
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How can i find the electric field due to a charged ring off-axis? Actually i have two ring electrodes in parallel and i would like to know how to find the electric field at any point in between the ring electrodes?
 
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  • #2
This is treated in advanced EM texts.
The steps for one ring are:
1. Find phi on ths axis.
2. Expand phi in a Taylor series for either z>a or z<a.
3. Use this expansion to write the Legendre polynomial expansion for all
angle. Use phi=\sum r^L P_L(cos\theta) (or 1/r^{L+1}).
4. Take grad phi to get E.
The result is a bit messy for two rings, but it can be done.
 
  • #3


To find the electric field at any point between the two charged ring electrodes, you can use the formula for the electric field due to a charged ring off-axis. This formula takes into account the distance from the point to the center of the ring, as well as the radius and charge of the ring. You can calculate the electric field at a specific point by plugging these values into the formula.

Additionally, you can use the principle of superposition to find the total electric field at a point between the two rings. This means that you can find the electric field due to each individual ring and then add them together to get the total electric field at that point.

It is important to note that the electric field between the two rings will not be uniform, as it will vary depending on the distance from each ring and the angles at which the electric fields from each ring intersect. Therefore, it may be helpful to break down the distance between the two rings into smaller sections and calculate the electric field at each section using the formula or the principle of superposition.

In summary, to find the electric field at any point between the two charged ring electrodes, you can use the formula for the electric field due to a charged ring off-axis and/or the principle of superposition. It is also important to consider the non-uniformity of the electric field and break down the distance between the two rings into smaller sections for more accurate calculations.
 

FAQ: Electric field due to a charged ring off-axis

1. What is the formula for calculating the electric field due to a charged ring off-axis?

The formula for calculating the electric field due to a charged ring off-axis is: E = (kQx)/(R^2 + x^2)^(3/2), where E is the electric field, k is the Coulomb constant, Q is the charge of the ring, x is the distance from the ring's center, and R is the radius of the ring.

2. How does the distance from the ring's center affect the electric field?

The electric field decreases as the distance from the ring's center increases. This is because the electric field follows an inverse square law, meaning that it decreases by the square of the distance. As you move further away from the ring, the electric field becomes weaker.

3. Is the electric field due to a charged ring off-axis affected by the charge of the ring?

Yes, the electric field is directly proportional to the charge of the ring. This means that as the charge of the ring increases, the electric field also increases. However, the formula for calculating the electric field takes into account the charge of the ring, so there is no need to make any additional calculations.

4. Can the electric field due to a charged ring off-axis be negative?

Yes, the electric field can be negative. This occurs when the charge of the ring is negative and the point in question is located on the opposite side of the ring. In this case, the electric field points towards the ring, making it negative.

5. How does the radius of the ring affect the electric field due to a charged ring off-axis?

The radius of the ring has a significant effect on the electric field. As the radius increases, the electric field becomes weaker. This is because the charge is spread out over a larger area, resulting in a smaller electric field. Conversely, as the radius decreases, the electric field becomes stronger.

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