Figure 22-40 shows two parallel nonconducting rings arranged with their central

Question

Figure 22-40 shows two parallel nonconducting rings arranged with their central axes along a common line. Ring 1 has uniform charge q1 and radius R; ring 2 has uniform charge q2 and the same radius R. The rings are separated by a distance d = 3.00R. The net electric field at point P on the common line, at distance R from ring 1, is zero. What is the ratio q1/q2?

Figure 22-40 shows two parallel nonconducting rings arranged with their central axes along a common line. Ring 1 has uniform charge q1 and radius R; ring 2 has uniform charge q2 and the same radius R. The rings are separated by a distance d = 3.00R. The net electric field at point P on the common line, at distance R from ring 1, is zero. What is the ratio q1/q2?

Explanation / Answer

E = F / q0 = mod(q) / 40*r^2

We use and assuming both charges are positive. at P, we have

E left ring = E right ring q1 R / 40(R^2+R^2)^3/2 = q2*2 R / 40(2R^2+R^2)^3/2

Simplifying, we obtain

q1 / q2 = 2(2/5)^3/2 = 0.506

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