Exercise 3:A nonuniform line charge distribution in the form of a half-circlewith a radius R is given by 1=1, sin 0 (2, is a constant) asdqRpresented in the following figure:1) Calculate the unit vectors (ur,ue) of the polar coordinatessystem as function of the unit vectors (i, j) in the rectangularcoordinates system. 2) By using the direct computation method, find the differential electric field dE that is created by adifferential charge (dq=2dl) in the center 0 of the half-circle in the rectangular coordinatessystem.3) Deduce the total electrical field in the center O of the half-circle. Notice that:1-cos(20)sin? (0):; sin (20)=2 sin (0)cos(0)24) If we assume that Q represents the total charge of the half-circle, proof that the total electric fieldE (0) =is given by:16 €,R

We have r^=cosθi+sinθj. Since θ^ is a rotation of r^ by an angle π2, we have…

Exercise 3: y A nonuniform line charge distribution in the form of a half-circle with a radius R is given by 1=1, sin 0 (2 is a constant) as dq R presented in the following figure: 1) Calculate the unit vectors (ur,ue) of the polar coordinates system as function of the unit vectors (i, j) in the rectangular coordinates system.

Exercise 3: y A nonuniform line charge distribution in the form of a half-circle with a radius R is given by 1=1, sin 0 (2 is a constant) as dq R presented in the following figure: 1) Calculate the unit vectors (ur,ue) of the polar coordinates system as function of the unit vectors (i, j) in the rectangular coordinates system.

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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