Two rings of radius 5cm are 20 cm apart and concentric with a common horizontal

Question

Two rings of radius 5cm are 20 cm apart and concentric with a common horizontal x-axis. the ring the left carries a distributed charge of + 31 nC, and the ring on the right carries a uniform distributed charge of-31 nC. What is the electric field due to the right ring at a location midway between the two rings? What is the electric field due to the left ring at a location midway between the two rings? What is the net electric field at a location midway between the two rings? If a charge of = 7 nC were placed midway between the rings, what would be the force exerted on this charge by the rings?

Explanation / Answer

Here,

r1 = 5 cm

x = 20 cm

q = 31 nC

part a) for the electric field due to right ring

electric field due to right ring = k * Q * x/(x^2 + r1^2)^(1.5)

electric field due to right ring = 9 *10^9 * 31 *10^-9 * (0.20/2)/sqrt(0.05^2 + 0.10^2)^(1.5)

electric field due to right ring = 746.3 N/C

part b) for the left ring

electric field due to left ring = k * Q * x/(x^2 + r1^2)^(1.5)

electric field due to left ring = 9 *10^9 * 31 *10^-9 * (0.20/2)/sqrt(0.05^2 + 0.10^2)^(1.5)

electric field due to left ring = 746.3 N/C

part c)

Now, for the net electric field between the rings

net electric field between the rings = E1 + E2

net electric field between the rings = 746.3 N/C + 746.3 N/nC

net electric field between the rings = 1492.6 N/C

part d)

q = -1 nc

net force on the charge = 1 *10^-9 * 1492.6

net force on the charge = 1.492 *10^-6 N

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