Electric field due to a charged ring off-axis

[a789irfan]

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?

 

[Meir Achuz]

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.

 

[astrokreng]

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.