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Three narrow concentric rings of radii 41 mm, 71 mm, and 94 mm are centered about the origin along the y - axis, with the axis of symmetry of each ring oriented along the y axis. The total charge on the inner ring is 1.8 µC, that on the middle ring is -1.0 µC, and that on the outer ring is 1.2 µC. What is the electric field magnitude (in N/C) at (0, 90 mm, 0)? Type in your answer in scientific format correct to one decimal place. Use a period for the decimal point. Do not use a comma. Scientific format is written as for eg. 1.2*10^8 to represent 1.2 × 10° Do NOT include units in your answer. Hint: You may assume that the electric field at a point y on the y-axis from a ring centered about the y-axis is given by Qu E (y) = k- (R²+y²){ where R is the radius of the ring and Q is the total charge on the ring in Coulombs.

Three narrow concentric rings of radii 41 mm, 71 mm, and 94 mm are centered about the origin along the y - axis, with the axis of symmetry of each ring oriented along the y axis. The total charge on the inner ring is 1.8 µC, that on the middle ring is -1.0 µC, and that on the outer ring is 1.2 µC. What is the electric field magnitude (in N/C) at (0, 90 mm, 0)? Type in your answer in scientific format correct to one decimal place. Use a period for the decimal point. Do not use a comma. Scientific format is written as for eg. 1.2*10^8 to represent 1.2 × 10° Do NOT include units in your answer. Hint: You may assume that the electric field at a point y on the y-axis from a ring centered about the y-axis is given by Qu E (y) = k- (R²+y²){ where R is the radius of the ring and Q is the total charge on the ring in Coulombs.

Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter19: Electric Forces And Electric Fields
Section: Chapter Questions
Problem 9OQ: Two solid spheres, both of radius 5 cm, carry identical total charges of 2 C. Sphere A is a good...
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Three narrow concentric rings of radii 41 mm, 71 mm, and 94 mm are centered about the origin along the y - axis, with the axis of symmetry of each ring oriented along the y axis. The total charge on the inner ring is 1.8 µC, that on the middle ring is -1.0 µC, and that on the outer ring is 1.2 µC. What is the electric field magnitude (in N/C) at (0, 90 mm, 0)? Type in your answer in scientific format correct to one decimal place. Use a period for the decimal point. Do not use a comma. Scientific format is written as for eg. 1.2*10^8 to represent 1.2 × 10° Do NOT include units in your answer. Hint: You may assume that the electric field at a point y on the y-axis from a ring centered about the y-axis is given by E (y) = k– Qy (R+y?)% where R is the radius of the ring and Q is the total charge on the ring in Coulombs. Type your answer.
Transcribed Image Text:Three narrow concentric rings of radii 41 mm, 71 mm, and 94 mm are centered about the origin along the y - axis, with the axis of symmetry of each ring oriented along the y axis. The total charge on the inner ring is 1.8 µC, that on the middle ring is -1.0 µC, and that on the outer ring is 1.2 µC. What is the electric field magnitude (in N/C) at (0, 90 mm, 0)? Type in your answer in scientific format correct to one decimal place. Use a period for the decimal point. Do not use a comma. Scientific format is written as for eg. 1.2*10^8 to represent 1.2 × 10° Do NOT include units in your answer. Hint: You may assume that the electric field at a point y on the y-axis from a ring centered about the y-axis is given by E (y) = k– Qy (R+y?)% where R is the radius of the ring and Q is the total charge on the ring in Coulombs. Type your answer.
Expert Solution
Step 1

Write the equation for electric field as below.

Ey=kQyR2+y232

Here, k is the Coulomb constant, R is the radius of the ring, y is the distance, and Q is the total charge on the ring in Coulombs.

 

Given data:

Radius of the ring, R1=41 mm=0.041 m=41×10-3 m

Radius of the ring, R2=71 mm=0.071 m=71×10-3 m

Radius of the ring, R3=94 mm=0.094 m=94×10-3 m

Distance, y=90 mm=0.09 m=90×10-3 m

The charge on the inner ring, Q1=1.8 μC=1.8×10-6 C

The charge on the middle ring, Q2=-1.0 μC=-1.0×10-6 C

The charge on the outer ring, Q3=1.2 μC=1.2×10-6 C

The Coulomb constant, k=9×109 N·m2C2

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