# Electric field of concentric rings

## Homework Statement

Derive the electric field a distance, z, above the center of a single uniformly charged ring of radius, R, with a linear charge density, λ. You are now given two uniformly charged concentric rings. The inner ring has radius, R, and carries a uniformly distributed total charge +[Q]. The outer ring has radius 3R and carries a uniform charge per length, λ. If the resulting electric field from the two rings is zero at an axial height of z=2R above the centers of the two rings, determine the value of λ.

Im wondering if I've solved for λ correctly

## Homework Equations

All relevant equations and work are attached in with clean typed images/work

## The Attempt at a Solution

All relevant equations and work are attached in with clean typed images/work

Thanks

#### Attachments

• Concentric Ring 1.png
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• Concentric Ring 2.png
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Delta2

Homework Helper
Gold Member
I think you have a mistake in the calculation of ##E_2##. The denominator should be ##{((2R)^2+(3R)^2)}^{3/2}##.

But I see no reason why you repeat the calculation. I mean you already found that the electric field at distance z above the centre due to a uniformed charged ring of radius R . Just apply this result for radius R=3R (if I can write it that way but I guess you ll understand what I mean).