Gauss's Law(differential form) | iTeachChem | Page 1

brave musk Jun 2, 2024, 6:55 AM

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How can we use differential form of Gauss's law for this qs?

tacit ravineBOT Jun 2, 2024, 6:55 AM

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<@&1227987967939838003>

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Note for OP

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brave musk Jun 2, 2024, 6:56 AM

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$$\nabla \cdot \vec{E} = \frac{\rho}{\epsilon_{0}}$$

celest ruin Jun 2, 2024, 6:56 AM

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Oh that's an amazing one

lyric canyonBOT Jun 2, 2024, 6:56 AM

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Keshav

brave musk Jun 2, 2024, 6:56 AM

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how to use this

celest ruin Jun 2, 2024, 6:58 AM

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Just a sec writing it down

brave musk Jun 2, 2024, 6:58 AM

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brave musk How can we use differential form of Gauss's law for this qs?

btw they have missed something
$$\vec{E} = \frac{a(x\hat{i}+y\hat{j})}{x^2+y^2}$$

lyric canyonBOT Jun 2, 2024, 6:58 AM

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Keshav

brave musk Jun 2, 2024, 6:59 AM

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this is the given expression

brave musk Jun 2, 2024, 7:02 AM

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celest ruin Just a sec writing it down

ohk

celest ruin Jun 2, 2024, 7:02 AM

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Oh there's an a

brave musk Jun 2, 2024, 7:03 AM

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that won't change a lot of things

celest ruin Jun 2, 2024, 7:03 AM

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Wait, is it necessary to use differential form? I'm using integral form rn. Just a sec

brave musk Jun 2, 2024, 7:03 AM

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uh, ik how to solve this using integral form
but was curious if we can use differential form as we have the expression for Electric field

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@celest ruin

celest ruin Jun 2, 2024, 7:10 AM

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Hmm I'm having trouble with the final integral

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What did you get divergence of E to be?

brave musk Jun 2, 2024, 7:14 AM

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$$div\cdot\vec{E}= \frac{\partial E_{x}}{\partial x} + \frac{\partial E_{y}}{\partial y}$$

lyric canyonBOT Jun 2, 2024, 7:14 AM

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Keshav

brave musk Jun 2, 2024, 7:16 AM

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bhai @celest ruin div 0 aa rha 💀
check kr toh

celest ruin Jun 2, 2024, 7:16 AM

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lyric canyon **Keshav**

Not this. I mean the final value.

celest ruin Jun 2, 2024, 7:17 AM

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brave musk bhai <@763645886500175892> div 0 aa rha 💀 check kr toh

Haan because origin pe infinite charge banega

brave musk Jun 2, 2024, 7:17 AM

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so this doesn't works

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@celest ruin so is it impossible to use this equation?

celest ruin Jun 2, 2024, 7:20 AM

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Mostly

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Divergence is infinite at origin.
$$\frac{4}{x^2+y^2}$$

lyric canyonBOT Jun 2, 2024, 7:21 AM

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Opt

brave musk Jun 2, 2024, 7:21 AM

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4/x^2+y^2??

celest ruin Jun 2, 2024, 7:22 AM

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Yup

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Wahi toh aata hai differentiation karne par, right?

brave musk Jun 2, 2024, 7:23 AM

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mera result 0 aa rha tha

celest ruin Jun 2, 2024, 7:23 AM

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$$\nabla$$

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Ok I haven't used LaTex before. Need to learn.

lyric canyonBOT Jun 2, 2024, 7:23 AM

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Opt

celest ruin Jun 2, 2024, 7:24 AM

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Anyways, zero nahi aata

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Varying with distance from origin. No chance the divergence is zero.

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Distance from z-axis sorry

brave musk Jun 2, 2024, 7:25 AM

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ok so if you result is correct what next?
$$\rho = \frac{Q}{4\pi a^2}$$

lyric canyonBOT Jun 2, 2024, 7:25 AM

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Keshav

celest ruin Jun 2, 2024, 7:25 AM

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Nope. That's wrong

brave musk Jun 2, 2024, 7:25 AM

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oh yeah

celest ruin Jun 2, 2024, 7:26 AM

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You have to integrate on the volume. Directly substituting is impossible.

brave musk Jun 2, 2024, 7:27 AM

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its making it harder lol
ig this equation is just making things harder for us

celest ruin Jun 2, 2024, 7:27 AM

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Yeah integral form is probably best here

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Because origin is out of the equation if you only consider surface integral

brave musk Jun 2, 2024, 7:28 AM

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yup

celest ruin Jun 2, 2024, 7:28 AM

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No zeroes in denominator.

brave musk Jun 2, 2024, 7:28 AM

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+solved @celest ruin

#Gauss's Law(differential form)