Three narrow concentric rings of radii 50 mmmm, 70 mmmm, and 90 mmmm are centered about the origin, with the axis of symmetry of each ring oriented along the yy axis. The charge on the inner ring is 1.5 μCμC , that on the middle ring is -1.7 μCμC , and that on the outer ring is 2.0 μCμC . What is the electric field magnitude at (0, 100 mmmm, 0)? Express your answer with the appropriate units. What quantity of charge must be placed at (0, -100 mmmm, 0) to make the electric field magnitude zero at the position calculated in the previous part? Express your answer with the appropriate units.

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Three narrow concentric rings of radii 50 mmmm, 70 mmmm, and 90 mmmm are centered about the origin, with the axis of symmetry of each ring oriented along the yy axis. The charge on the inner ring is 1.5 μCμC , that on the middle ring is -1.7 μCμC , and that on the outer ring is 2.0 μCμC .

What is the electric field magnitude at (0, 100 mmmm, 0)?
Express your answer with the appropriate units.
What quantity of charge must be placed at (0, -100 mmmm, 0) to make the electric field magnitude zero at the position calculated in the previous part?
Express your answer with the appropriate units.
Expert Solution
Step 1

The electric field at a distance z from the center of a ring of radius r and having charge q is given asE=q4πεozz2+r23/2

First ring having radius 50 mm or 0.05 m will have electric field given asE1=q4πεozz2+r23/2z=100 mm or 0.1 mr=0.05 mq=1.5 μC=1.5×10-6 CE1=9×109×1.5×10-6×0.10.12+0.0523/2E1=13.5×103×0.10.01253/2E1=13.5×103×0.11.3975×10-3E1=13.5×103×71.5542E1=965.9814×103 N/C

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