A non-conducting ring has a radius r and a constant charge distribution of lambda

Sunday, 12 August 2018

6:20 PM

Machine generated alternative text: Question: A non-conducting ring nas a radius r and a constant charge distribution ot In this question you are going to derive an expression tor the electric field a distance a above the centre of the ring. use unit vector notation tor your answers, the direction of the unit vectors is shown in the diagram. use Coulomb's constant in your answer, denoted by k, do not use €0. i a ds Figure 1. A charged ring ot radius r and uniform charge density sits on the x, y-axis. A point lies on the z-axis a distance a above the ring. The ring can be broken into increments witn length part 1) Consider the increment shown in Figure 1 witn length ds. IT is located at ri m. Write an expression to describe the electric field at the point due to the increment ds. dEds =( dsi+ dsj

Machine generated alternative text: part 2) a ds ds with charge dq Figure 2. The ring can be broken up into infinitesimal segments ds and charge dq We will need to add all the increments around this ring. This is easiest to do in pairs. What is the electric field at the point due to the pair ot increments ds found at ri and dE2ds part 3) dsi+ ay summing all the increments in pairs around the ring or othenvise, derive an expression for the electric field a distance a m above the centre ot the ring. +1 j

 

Machine generated alternative text: Your answer is partially correct Feedback tor Part 1) You have incorrectly entered the first component You have correctly entered the second component You have incorrectly entered the third component The electric field due to a point q C a distance d m away is given by: In this case, q = ds and d a2 + r2, using Pythagoras theorem. dE Now we need to consider the geometry: Ecos9 4TEo d2 Ads (a2+r2) • E Esine 9 r 1, 2 a dc Figure 1. In the x, z-plane the electric field can be broken up into and z components. In the figure: cos(9) v/a2 + r2 sin(9) — v/a2 + r2

 

Machine generated alternative text: dE = k Ads a24_r2 k Ads v/a2 + r2 v/a2 + r2 Ads (a2 +r2)3/2 Marks for this submissiom 0.11/0.33. This submission attracted a penalty of 0.11 Feedback tor Part 2) You have correctly entered the first component You have correctly entered the second component You have correctly entered the third component. Marks for this submissiom 0.33/0.33. Feedback tor Part 3) You have correctly entered the first component You have correctly entered the second component You have correctly entered the third component. Marks for this submissiom 0.33/0.33. —ri + ak

 

Machine generated alternative text: A correct answer — , which can be typed in as follows: 402) A correct answer is O, which can be typed in as follows: A correct answer is , which can be typed in as follows: 4a2) A correct answer is O, which can be typed in as follows: A correct answer is O, which can be typed in as follows: 20 •k A A correct answer , which can be typed in as follows: A correct answer is 0, which can be typed in as follows: A correct answer is 0, which can be typed in as follows: A correct answer is , which can be typed in as follows:

 

 

Created with Microsoft OneNote 2016.