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Problem 54 Hard Difficulty

A very large nonconducting plate lying in the $x$ -plane carries a charge per unit area of $\sigma .$ A second such plate located at $z=2.00 \mathrm{cm}$ and oriented parallel to the $x$ y-plane carries a charge per unit area ol $-2 \sigma .$ Find the electric lield (a) for $z<0,$ (b) $0<z<2.00 \mathrm{cm},$ and $(\mathrm{c}) z>2.00 \mathrm{cm} .$

Answer

a. $\frac{+\sigma}{2 \varepsilon_{0}}$
b. $\frac{\sqrt{3 \sigma}}{2 \varepsilon_{0}}$
c. $\frac{\overline{2} \sigma}{2 \varepsilon_{0}}$
d. $\frac{-\sigma}{2 \varepsilon_{0}}$

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JC

Julio C.

September 14, 2020

An infinite plate, with a positive charge per unit area equal to ?, is in the xz plane. A second infinite plate, with a negative charge per unit area ?? is on the xy plane. Get the potential difference between points a = (1, 1, 1) and b = (2, 2, 2)

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Video Transcript

harassed Rain slash Start our discussion. Suppose you have a coordinate system X Y jet plane. Okay. Now, in the X Y plane there are there are known conducting place. Okay. At Jackie's, it goes to digital. There's a play who have a charge Density off sigma and a jab. Physicals to door centimeter days a plate off charge density minus two sigma. Now you have to find out the electric field or over the region's jet. Lest Anjiro jet greater than zero, but less than two centimeter and gel greater than two centimeters. Okay, so let's divide this range in three areas. This is our first region. This is our second region. And this is our provision. So first of all, I want to tell you that electric field due to a charge, it is Sigma upon to ab Silent north. Okay, if I'm taking the magnitude so see, this is the positive charge density, which means that charge on this shit is positive. And charging this city is negative. So basically in region first that elect If I name this year one and this year too. So in the region, first electric field due to one is in this direction, he wouldn't. And in this region, electric field you toe to isn't a poor direction, Ito, because electric will always comes from positive and go towards negative. Okay, in regions sacking the electric field even isn't this direction. And e two is also in this direction. InVision free electric field due to world is in this direction. But electrically do toe to is in this direction. No, we have to find out that neck electric field and bought these regions. So basically, Natalie, like if I'm assuming a full electric feel bean positive jet access and nag indoor more electric for being negative. Jack, Texas. Okay, so basically net electric field. So in it in the first region is even minus Kick it. Plus you do positive Get cap that is getting okay. So Sigma upon the web. Silent note plus two sigma upon the website and note. So by soul will this we will get a net electric field or Sigma two AB silent note in positive care direction. Okay, this isn't vector ful. Okay, Now in the region, second in the region. Second, if you see the figure even is in positive change direction and e two is also in positive direction. Okay, so it is Sigma pawn tohave silent note blurs the one Sigma pawn tohave silent note. So the net electrical in the real second is Preeb. Silent Lord treats sigma upon toe outside a note in positive direction. Okay, Right in the region, third in the region. Tard even is in positive jack direction. But he too isn't negative jet direction. So it will be Sigma pawn toe Upsell in north K cap minus two Sigma pawn to epsilon. Note K cap. So it will comes Toby. Minus sigma pronto. Absolute North K cap, that is sick. Mark on toe. Absolute note, minus giga. That is it. Net electric feel in the third region isn't negative. Jet direction. Well, this is all for me for this video. I hope you will like the video. Thank you.

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Andy C.

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