Potential V and E field of 2 rings of charge on x axis

there are 2 rings of charge, radius R on the x axis separated by a distance R, find the potential and E field.

so don't you have to calculate the field to the left of the 2 rings, in between the 2 rings and to the right? I get these answers for the E field which by symmetry points only on the x axis away from the rings. in the area to the left and to the right of the rings the 2 fields will add and in between there will be some subtraction

I think my calculation is off here, the field for one ring, positive lambda charge pointing away from the ring is?

calculate only the field on the x axis, the absolute value of the fields to the left and to the right of 2 rings are equal

for V to the right of 2 rings:

for V to the left of the 2 rings, is the potential thus, or can I use a potential from -infinity to x3 the point intersecting the left ring?

Re: Potential V and E field of 2 rings of charge on x axis

Quote:

Originally Posted by

**mathnerd15** there are 2 rings of charge, radius R on the x axis separated by a distance R, find the potential and E field.

so don't you have to calculate the field to the left of the 2 rings, in between the 2 rings and to the right? I get these answers for the E field which by symmetry points only on the x axis away from the rings. in the area to the left and to the right of the rings the 2 fields will add and in between there will be some subtraction

I think my calculation is off here, the field for one ring, positive lambda charge pointing away from the ring is?

First let's clean up the notation a bit. The radius of your rings and distance between rings is R not r, according to your problem statement. And the permittivity of free space has a subscript:0

Now, this is the equation for the electric field of a ring of charge in the yz plane centered at the origin. We have a choice: to place the second ring at x = R or to center the rings at x = +/- R/2. I'm going to go with the more symmetrical +/-R. I'm also going to assume that both rings have the same signed charge. That is to say I'm assuming both rings have charge +q.

The field of the ring at x = -R/2 will be the ring of charge equation translated by R/2:

Likewise for the ring at x = +R/2:

So do you put these together? (Remember that E is a *vector*.)

-Dan