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iTeachChem•7mo ago

Potential maybe?

Have also attached my futile approach help please

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iiTeachChem / 💭│doubts

iiTeachChem / 💭│doubts

iiTeachChem / 💭│doubts

iiTeachChem / 💭│doubts

iTeachChem Helper

I

iTeachChem Helper•5/31/25, 6:49 PM

@Gyro Gearloose

iTeachChem Helper

I

iTeachChem Helper•5/31/25, 6:49 PM

Note for OP

+solved @user1 @user2...+solved @user1 @user2... to close the thread when your doubt is solved. Mention the users who helped you solve the doubt. This will be added to their stats.

wilted_flower

Wwilted_flower Have also attached my futile approach help please

Opt

O

Opt•5/31/25, 6:50 PM

Direct Laplace equation

Sephrina

S

Sephrina•5/31/25, 6:51 PM

the what eqn

Opt

O

Opt•5/31/25, 6:51 PM

$$\nabla^{2}V = \frac{-\rho}{\epsilon}$$

Opt

O

Opt•5/31/25, 6:52 PM

In your case, since V doesn't depend on theta and phi, it simplifies

Sephrina

S

Sephrina•5/31/25, 6:52 PM

in which chap is this eqn in book i hve never seen this

Sephrina

SSephrina in which chap is this eqn in book i hve never seen this

Opt

O

Opt•5/31/25, 6:53 PM

It's Gauss' Law in differential form combined with E = -dV/dr

Opt

O

Opt•5/31/25, 6:53 PM

OOPS

Opt

O

Opt•5/31/25, 6:53 PM

Wait

TeXit

T

TeXit•5/31/25, 6:53 PM

Opt

Opt

OOpt It's Gauss' Law in differential form combined with E = -dV/dr

Sephrina

S

Sephrina•5/31/25, 6:54 PM

never seen this i need to read up more on this stuff

Opt

O

Opt•5/31/25, 6:54 PM

Sorry, I missed the minus sign

Sephrina

SSephrina never seen this i need to read up more on this stuff

Opt

O

Opt•5/31/25, 6:54 PM

It's fine, you can do without that

Opt

OOpt It's fine, you can do without that

Sephrina

S

Sephrina•5/31/25, 6:54 PM

thnk god because partial differntiations just... scare me

Opt

O

Opt•5/31/25, 6:54 PM

You just do it in two steps basically

Sephrina

SSephrina thnk god because partial differntiations just... scare me

Opt

O

Opt•5/31/25, 6:54 PM

Here because there's no theta or phi, it's a simple derivative only

Sephrina

S

Sephrina•5/31/25, 6:54 PM

thts great though

wilted_flower

W

wilted_flowerOP•5/31/25, 6:55 PM

The hell is all this

wilted_flower

W

wilted_flowerOP•5/31/25, 6:55 PM

Laplace was in Thermodynamics

Sephrina

S

Sephrina•5/31/25, 6:55 PM

i suck at simple diffrential at times

wilted_flower

W

wilted_flowerOP•5/31/25, 6:55 PM

Iirc

Opt

O

Opt•5/31/25, 6:55 PM

$$\frac{d^{2}V}{dr^{2}}=\frac{-\rho}{\epsilon}$$

TeXit

T

TeXit•5/31/25, 6:55 PM

Opt

wilted_flower

Wwilted_flower The hell is all this

Sephrina

S

Sephrina•5/31/25, 6:55 PM

exct my rxn

Opt

OOpt $$\frac{d^{2}V}{dr^{2}}=\frac{-\rho}{\epsilon}$$

Sephrina

S

Sephrina•5/31/25, 6:55 PM

so we integrate both sides to get the result here?

Sephrina

SSephrina so we integrate both sides to get the result here?

Opt

O

Opt•5/31/25, 6:55 PM

No, no need

Opt

O

Opt•5/31/25, 6:55 PM

It's rho that is asked

Opt

O

Opt•5/31/25, 6:56 PM

So differentiate V twice and multiply by epsilon

Opt

O

Opt•5/31/25, 6:56 PM

Should give answer

Sephrina

S

Sephrina•5/31/25, 6:56 PM

aah easy

Sephrina

S

Sephrina•5/31/25, 6:56 PM

i will try now

wilted_flower

W

wilted_flowerOP•5/31/25, 6:56 PM

Opt bhai samaanya aam simple bhasha me bata do kuch

wilted_flower

Wwilted_flower Opt bhai samaanya aam simple bhasha me bata do kuch

Opt

O

Opt•5/31/25, 6:56 PM

Ok, I'll explain it in a way that's mathematically wrong, but simple to understand

Opt

O

Opt•5/31/25, 6:57 PM

E × A = q/e (I'll use e for epsilon)

Sephrina

S

Sephrina•5/31/25, 6:57 PM

if i am not diffrential dumb it should be 4a (epslon not)

Sephrina

SSephrina if i am not diffrential dumb it should be 4a (epslon not)

wilted_flower

W

wilted_flowerOP•5/31/25, 6:58 PM

No ye to gauss law hai

Sephrina

S

Sephrina•5/31/25, 6:58 PM

final ans bolri hu

Opt

O

Opt•5/31/25, 6:58 PM

E × A × e = q

Divide by volume

E × e/l = rho

But E = -V/l

-V/l × e/l = rho

Rho = -e(d²V/dr²)

Dimensions are correct

wilted_flower

W

wilted_flowerOP•5/31/25, 6:59 PM

Woah

wilted_flower

W

wilted_flowerOP•5/31/25, 6:59 PM

Crwazy

Sephrina

S

Sephrina•5/31/25, 6:59 PM

mujhe isse samjhne do

Sephrina

S

Sephrina•5/31/25, 6:59 PM

10 min lagega

wilted_flower

W

wilted_flowerOP•5/31/25, 6:59 PM

How are supposed to figure this out in the exam again?

wilted_flower

W

wilted_flowerOP•5/31/25, 6:59 PM

Sephrina

S

Sephrina•5/31/25, 6:59 PM

good question

Opt

O

Opt•5/31/25, 6:59 PM

Opt

OOpt ||Any person who has studied vector calc will sue me for this bakwaas explanatio...

wilted_flower

W

wilted_flowerOP•5/31/25, 7:00 PM

I fortunately haven't so yea lucky day

Opt

OOpt E × A × e = q Divide by volume E × e/l = rho But E = -V/l -V/l × e/l = rho ...

Sephrina

S

Sephrina•5/31/25, 7:00 PM

i didnt get the last step

Opt

O

Opt•5/31/25, 7:00 PM

Actual explanation is that Gauss' Law, which is integral as taught to you guys, can also be written in a differential form.

+solved @user1 @user2...

+solved @user1 @user2...