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A plastic rod 1.7 m long is rubbed all over with wool, and acquires a charge of -8E-8 coulombs. We choose the center of the rod to be the origin of our coordinate system, with the x-axis extending to the right, the y-axis extending up, and the z-axis out of the page. In order to calculate the electric field at location A = < 0.7,0,0> m, we divide the rod into 8 pieces, and approximate each piece as a point charge located at the center of the piece. a h b 12345678 || | || | || i A (a) What is the length of one of these pieces? Save for Later i i g d j zero magnitude (b) What is the location of the center of piece number 2? m i (c) How much charge is on piece number 2? (Remember that the charge is negative.) coulombs i (d) Approximating piece 2 as a point charge, what is the electric field at location A due only to piece 2? E₂ = < i > m. i > N/C

A plastic rod 1.7 m long is rubbed all over with wool, and acquires a charge of -8E-8 coulombs. We choose the center of the rod to be the origin of our coordinate system, with the x-axis extending to the right, the y-axis extending up, and the z-axis out of the page. In order to calculate the electric field at location A = < 0.7,0,0> m, we divide the rod into 8 pieces, and approximate each piece as a point charge located at the center of the piece. a h b 12345678 || | || | || i A (a) What is the length of one of these pieces? Save for Later i i g d j zero magnitude (b) What is the location of the center of piece number 2? m i (c) How much charge is on piece number 2? (Remember that the charge is negative.) coulombs i (d) Approximating piece 2 as a point charge, what is the electric field at location A due only to piece 2? E₂ = < i > m. i > N/C

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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A plastic rod 1.7 m long is rubbed all over with wool, and acquires a charge of -8E-8 coulombs. We choose the center of the rod to be the origin of our coordinate system, with the x-axis extending to the right, the y-axis extending up, and the z-axis out of the page. In order to calculate the electric field at location A = < 0.7,0,0> m, we divide the rod into 8 pieces, and approximate each piece as a point charge located at the center of the piece. a h b || | || | 2 3 4 5 6 i A (a) What is the length of one of these pieces? Save for Later i i g d j zero magnitude (b) What is the location of the center of piece number 2? m i (c) How much charge is on piece number 2? (Remember that the charge is negative.) coulombs i (d) Approximating piece 2 as a point charge, what is the electric field at location A due only to piece 2? E₂ = < i > m. i > N/C (e) To get the net electric field at location A, we would need to calculate due each of the 8 pieces, and add up these contributions. If we did that, which arrow above would best represent the direction of the net electric field at location A?
Transcribed Image Text:A plastic rod 1.7 m long is rubbed all over with wool, and acquires a charge of -8E-8 coulombs. We choose the center of the rod to be the origin of our coordinate system, with the x-axis extending to the right, the y-axis extending up, and the z-axis out of the page. In order to calculate the electric field at location A = < 0.7,0,0> m, we divide the rod into 8 pieces, and approximate each piece as a point charge located at the center of the piece. a h b || | || | 2 3 4 5 6 i A (a) What is the length of one of these pieces? Save for Later i i g d j zero magnitude (b) What is the location of the center of piece number 2? m i (c) How much charge is on piece number 2? (Remember that the charge is negative.) coulombs i (d) Approximating piece 2 as a point charge, what is the electric field at location A due only to piece 2? E₂ = < i > m. i > N/C (e) To get the net electric field at location A, we would need to calculate due each of the 8 pieces, and add up these contributions. If we did that, which arrow above would best represent the direction of the net electric field at location A?
Expert Solution
Step 1

(A) Total length of 1.7 m is divided into eight parts hence length of one piece will be (1.7/8) = 0.2125 m 

(B) As origin is at point 4, the distance of point 2 from point 4 will be 3 unit up, that's means point 2 is ( 0.2125×3) = 0.6375 m .

As point 2 lies on y axis it's vector notation will be (0x + 0.6325 y+ 0z) = ( 0,0.6325, 0). 

(C)  total charge on sheet =- 8× 10^-8 C. 

Since all sheet are identical, the charge distribution on all the points will be same. 

Charge on point 2 =( -8×10^-8 C)/9=  -0.89 ×10^-8 C. 

(D) The net electric field will be towards the point 2 as the charge is negative. 

E = (K Q /R^2 )

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