Finding the Electric Field at the Midpoint of two rings

AI Thread Summary
To find the electric field at the midpoint between two charged rings, the principle of superposition is applied. The left ring has a charge of -22 nC and the right ring +22 nC, both 10 cm from the midpoint. The electric field contributions from each ring cancel at the midpoint due to symmetry, resulting in a net electric field of zero. The correct approach involves recognizing that the field at the center of each ring is zero, and thus the total electric field at the midpoint is also zero. Understanding the distribution of charge around a ring is crucial for solving this problem correctly.
arileah
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Homework Statement


Hello,

Two 10-cm-diameter charged rings face each other, 20 cm apart. The left ring is charged to -22 nC and the right ring is charged to +22 nC . What is the magnitude of the electric field E⃗ at the midpoint between the two rings?

Homework Equations


[/B]
E = Kq/r^2
K = 8.99 * 10^9

The Attempt at a Solution



Find the electric field at the midpoint caused by each individual plate, then using the principle of superposition to add them.

E(tot) = |E(1)| + |E(2)|

|E(1)| = K (22nC)/0.1^2
|E(2)| = K (22nc)/0.1^2

|E(1)| + |E(2)| = E {since E(1) and E(2) are the same}

E(tot) = E = 2 * K (22nC)/0.1^2 = 395560 N/C

However, the answer I got is wrong. I have also tried E = 0 N/C in case I was not supposed to take the magnitudes. This is also incorrect.

Could anyone lend me a hand?
 
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arileah said:
K (22nC)/0.1^2
That would be the field 10cm from a point charge of 22nC.
The charge here is distributed around a ring (not a plate). At the centre of each ring there is no field induced by that ring since the fields due to the charges around the ring point in all directions through the centre and, by symmetry, cancel.
Consider a small portion of one ring, length rdθ, carrying charge q, where r is the ring's radius. And consider a point P distance x from the centre of the ring, along the axis of the ring. How far is P from the charge q? What is the strength of the field at P due to the charge q? In what direction does that field point?

Alternatively, you may have already been taught a formula for the axial field due to one ring, in which case all you have to do is double it for the second ring.
 
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Thank you! I got it now :)
 
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