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Q1. A curved plastic rod of charge +Q forms a semi-circle of radius R in the x-y plane, as shown below on the left. The charge is distributed uniformly across the rod. dQ Now let's analytically determine the magnitude and direction of the electric field E at the center of the circle using polar coordinates and the charge element dQ shown in the image on the right.

Q1. A curved plastic rod of charge +Q forms a semi-circle of radius R in the x-y plane, as shown below on the left. The charge is distributed uniformly across the rod. dQ Now let's analytically determine the magnitude and direction of the electric field E at the center of the circle using polar coordinates and the charge element dQ shown in the image on the right.

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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PO Lab2part1.pdf po Tutorial2_212.pdf O File | C:/Users/alvin/OneDrive/Desktop/Penn%20State/Spring%202021/PHYS%20212/Tutorial%202/Tutorial2_212.pdf Not syncing of 2 + (D Page view A Read aloud V Draw F Highlight 1 Erase Phys 212 Tutorial 02 Electric field from continuous distributions of charge. Name: Q1. A curved plastic rod of charge +Q forms a semi-circle of radius R in the x-y plane, as shown below on the left. The charge is distributed uniformly across the rod. dQ +Q +Q R Now let's analytically determine the magnitude and direction of the electric field E at the center of the circle using polar coordinates and the charge element dQ shown in the image on the right. Write down an expression for the electric field dE at the center of the circle due to this element dQ. Hints: a. Remember, dE is a vector, write using the î, ĵ notation. b. your answer should be written in terms of R, 0 a. c. use that dQ = a dl where now 2 is the linear charge density 1 = 2 (total charge/divided by total length). d. use polar coordinates where dl = Rd0 b. Write down the integral you need to do to solve for Ex and E, at the center of the semi-circle (be sure to specify the limits of integration). 7:02 PM e Type here to search 口 Lr Ps 2/2/2021 22ת
Transcribed Image Text:PO Lab2part1.pdf po Tutorial2_212.pdf O File | C:/Users/alvin/OneDrive/Desktop/Penn%20State/Spring%202021/PHYS%20212/Tutorial%202/Tutorial2_212.pdf Not syncing of 2 + (D Page view A Read aloud V Draw F Highlight 1 Erase Phys 212 Tutorial 02 Electric field from continuous distributions of charge. Name: Q1. A curved plastic rod of charge +Q forms a semi-circle of radius R in the x-y plane, as shown below on the left. The charge is distributed uniformly across the rod. dQ +Q +Q R Now let's analytically determine the magnitude and direction of the electric field E at the center of the circle using polar coordinates and the charge element dQ shown in the image on the right. Write down an expression for the electric field dE at the center of the circle due to this element dQ. Hints: a. Remember, dE is a vector, write using the î, ĵ notation. b. your answer should be written in terms of R, 0 a. c. use that dQ = a dl where now 2 is the linear charge density 1 = 2 (total charge/divided by total length). d. use polar coordinates where dl = Rd0 b. Write down the integral you need to do to solve for Ex and E, at the center of the semi-circle (be sure to specify the limits of integration). 7:02 PM e Type here to search 口 Lr Ps 2/2/2021 22ת
PO Lab2part1.pdf po Tutorial2_212.pdf O File | C:/Users/alvin/OneDrive/Desktop/Penn%20State/Spring%202021/PHYS%20212/Tutorial%202/Tutorial2_212.pdf Not syncing of 2 + (D Page view A Read aloud V Draw F Highlight 2 Erase What are the result of these two integrals? You may need to use f cos 0 d0 = sin 0 and | sin 0 de = - cos 0 C. d. What is the magnitude of the total E field at the center? e. Using a symmetry argument, what will be the E field at the center created by a negatively charged half ring in the bottom half? Q2. Context Rich Problem. This question requires you to put everything from Q1 together. No new calculations needed. You are helping to design a new electron microscope to investigate the structure of the HIV virus. A new device to position the electron beam consists of a charged circle of conductor. This circle is divided into two half circles separated by a thin insulator so that half of the circle can be charged positively and half can be charged negatively. The electron beam will go through the center of the circle. To complete the design your job is to calculate the electric field in the center of the circle as a function of the amount of positive charge on the half circle, the amount of negative charge on the half circle, and the radius of the circle. 7:02 PM e Type here to search Lr Ps 2/2/2021 22ת
Transcribed Image Text:PO Lab2part1.pdf po Tutorial2_212.pdf O File | C:/Users/alvin/OneDrive/Desktop/Penn%20State/Spring%202021/PHYS%20212/Tutorial%202/Tutorial2_212.pdf Not syncing of 2 + (D Page view A Read aloud V Draw F Highlight 2 Erase What are the result of these two integrals? You may need to use f cos 0 d0 = sin 0 and | sin 0 de = - cos 0 C. d. What is the magnitude of the total E field at the center? e. Using a symmetry argument, what will be the E field at the center created by a negatively charged half ring in the bottom half? Q2. Context Rich Problem. This question requires you to put everything from Q1 together. No new calculations needed. You are helping to design a new electron microscope to investigate the structure of the HIV virus. A new device to position the electron beam consists of a charged circle of conductor. This circle is divided into two half circles separated by a thin insulator so that half of the circle can be charged positively and half can be charged negatively. The electron beam will go through the center of the circle. To complete the design your job is to calculate the electric field in the center of the circle as a function of the amount of positive charge on the half circle, the amount of negative charge on the half circle, and the radius of the circle. 7:02 PM e Type here to search Lr Ps 2/2/2021 22ת
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