Electric Field Between Two Charged Rings: Problem Solved

[Linus Pauling]

1. Two 10-cm-diameter charged rings face each other, 19.0 cm apart. Both rings are charged to + 50.0 nC. What is the electric field strength:

At the midpoint between the two rings? At the center of the left ring?



2. E = q/4pi*ep_o*r^2



3. The online problem says this is from a certain chapter in our book... that chapter (which we've read) is about point charges. Am I able to treat these things as point charges? I would think not given the small distances being considered... so think maybe it's a typo. Anyways, could someone outline the strategy for this type of problem?

 

[Linus Pauling]

Is the answer zero in both cases? Since they're both positively charged, the field lines will point into the space between the rings, but then curve upwards as they come together since they're the same sign, so the middle is zero? Likewise, the center of one ring is zero because the y component of the field from that ring cancels out?

 

[ideasrule]

The field at the midpoint is 0 because of the symmetry of the configuration. Likewise, the field at the center of a ring due to that ring is 0, again due to symmetry. You still have to consider the electric field produced by the other ring, which isn't 0.

 

[epenguin]

Well, if I remember, the field at a point is the force experienced by unit charge at the point so they could say point charges come into it, haw haw.

This one is asking for a minimum of physical intuition I guess. The first problem is very symmetrical. As preliminary, a still simpler situation, what is the net result force on a charge just half way between to equal point charges (both of the same sign)?

Moving on to the rings, you can assume the distribution of charge is uniform around the ring. Makes a very symmetrical situation.

In the second problem, the field is (still) the (vector, i.e. directional) sum of the field due to the two different rings. That from the ring it's in the centre of is an extremely symmetrical situation.

3/4 of the question requires no calculation really.

 

[epenguin]

2 other posts came in whilst I was typing mine. If you mean to say points equally distant from equal charges the field is zero, agreed.

Agree field from ring in its centre is zero. So that leaves you with only the second part of the second problem.