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Problem 50 Hard Difficulty

A charge of $q=2.00 \times 10^{-9} \mathrm{C}$ is spread evenly on a thin metal disk of radius 0.200 $\mathrm{m} .$ (a) Calculate the charge density on the disk. (b) Find the magnitude of the clectric ficld
just above the center of the disk, neglecting edge effects and assuming a uniform distribution of charge.

Answer

a. $1.59 \times 10^{-8} \mathrm{C} / \mathrm{m}^{2}$
b. 898.67 $\mathrm{N} / \mathrm{C}$

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Video Transcript

has to re insulin start or discussion. Suppose you have a matter disk, a circular metal disc and the charge You two in tow. Tenderest part minus nine. Column is spread evenly in this disc. Okay? And the radius off this case going do meter. Now you have to find out a charge Density off this disc. Basically, this disk is attended this so the charge density will be dancer physicals to surface star density does that well, johrj or unit area. Okay, so total charges to inter tend this par minus nine Coolum and the area is by 90.2 square. If you solve this, you will get a value 1.59 in tow. 10 this part minus eight. Coolum. Poor meter square. This is the charge into your disc. Okay? No. Suppose you have to find out the electric field just above off the disk. So basically, if this is the point B, no, you have to find out the electric field due to distaste on this point B. Okay. This distance is a Okay. No, here. This the charges uniformly distributed over the desk. Okay, So for this, we have to taken Adam mental disk support off radius X Baltacha Elemental drink on that sickness of their English DX. And is it? This tends acts from the center The radios off the core discus are okay now, electric feel due to this elemental jing act point B is Val upon foot by up silent north charge in clothes that is dick you by X squared Bless a square. Okay, this is the electric field by the elemental ring. But we have to find out the city. We have to find out the electric field at b Do the whole disk so forth This we have to integrate it. So basically, if ah in the are a chest the value of dick you is actually the interest sigma. Okay. And the area element is to buy eggs The eggs signal Where signifies that charge Density off the disc surface Charge Density of the decks, Sir Dick, you will be Dubai acts the X Sigma. So if I to buy Sigma x the X by x square plus a square Okay. And integration lies from Joe toe because areas off discuss Okay. No, If I was, I saw this further by will be Can slope and a Sigma by two upside north. And for this integration, I have toe take musicals too X square plus a square. So that date it will be two x dx. Okay, so it will comes to obey Davey one by two comes out and p. Actually it's power three, but I do Okay, see by. And this is the limit limit off X No, we have to change in the limit off key. So basically at access it goes to Jiro. He will be a square and at exit sickles to ah, he will be a square plus exquisite. Ask what? Okay, so it will be a square plus a square. Bless our square. Now, after Seoul, will this integration? We will get the final answer. That is baggage off electric field over. Um some certain point A will be Sigma bike Web Silent Lord one minus a upon our square plus a square power three by two Newton. But cool. This is the man into low fee. So by putting the value of child density and some distance at which we have to find the electric field and by putting the radius off the electric field we will get the value off electric feel at point just above that disk. Well, this is all for me for this video. I hope you will like the really a tank.

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Top Physics 102 Electricity and Magnetism Educators
Elyse G.

Cornell University

Zachary M.

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Aspen F.

University of Sheffield

Jared E.

University of Winnipeg

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Join Bootcamp