iTeachChem•9mo ago

gauss law

a hollow insulating sphere contains a point charge +q are its centre, find force between them

iTeachChem Helper•4/13/25, 12:02 PM

@Gyro Gearloose

iTeachChem Helper•4/13/25, 12:02 PM

Note for OP

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Opt•4/13/25, 12:03 PM

Is the insulating sphere charged as well?

OOpt Is the insulating sphere charged as well?

AetherflyOP•4/13/25, 12:03 PM

yes +Q

Opt•4/13/25, 12:04 PM

There's no force either way I'm pretty sure

AetherflyOP•4/13/25, 12:05 PM

yeah sorry for being dumb but what mistake am i doing here

Opt•4/13/25, 12:05 PM

Force on point charge is zero, and by Newton's third law, force on spherical shell should also be zero

OOpt Force on point charge is zero, and by Newton's third law, force on spherical she...

AetherflyOP•4/13/25, 12:05 PM

exactly

AAetherfly yeah sorry for being dumb but what mistake am i doing here

SirLancelotDuLac•4/13/25, 12:06 PM

The integral thing mein you are treating a vector as a scalar.

AAetherfly yeah sorry for being dumb but what mistake am i doing here

Opt•4/13/25, 12:06 PM

Ah, but the thing is, ʃE dS is not flux

Flux is ʃE•dS

SSirLancelotDuLac The integral thing mein you are treating a vector as a scalar.

AetherflyOP•4/13/25, 12:06 PM

it should be EdS cos theta but theta = 0

SirLancelotDuLac•4/13/25, 12:06 PM

E.dS doesn't add up, rather adds vectorally cancelling out.

Opt•4/13/25, 12:06 PM

Just the integral is zero since corresponding opposite field vectors cancel out

OOpt Ah, but the thing is, ʃE dS is not flux Flux is ʃE•dS

AetherflyOP•4/13/25, 12:07 PM

but E dot dS is always positive

AetherflyOP•4/13/25, 12:07 PM

for any dS

AAetherfly but E dot dS is always positive

Opt•4/13/25, 12:07 PM

Yes. Here you're not doing the dot product

AetherflyOP•4/13/25, 12:07 PM

but uh E dS costheta = E dot dS right??

OOpt Yes. Here you're not doing the dot product

AetherflyOP•4/13/25, 12:08 PM

i mightve confused this with the plate qn

AetherflyOP•4/13/25, 12:08 PM

have you done the square plate qn?

AetherflyOP•4/13/25, 12:10 PM

AAetherfly but uh E dS costheta = E dot dS right??

Opt•4/13/25, 12:11 PM

There's no cosθ here though

OOpt There's no cosθ here though

AetherflyOP•4/13/25, 12:11 PM

like uh cos theta = 1 cuz angle b/w field and dS is 0

Opt•4/13/25, 12:11 PM

Also, see it this way. Are you not integrating for the force?

Opt•4/13/25, 12:11 PM

And force is a vector

Opt•4/13/25, 12:11 PM

So if your answer is a scalar....

Opt•4/13/25, 12:11 PM

Surely there's some mistake right?

OOpt Surely there's some mistake right?

AetherflyOP•4/13/25, 12:11 PM

yes

Opt•4/13/25, 12:12 PM

And that mistake is that here you're integrating Edq correct?

Opt•4/13/25, 12:12 PM

Bold is vector

Opt•4/13/25, 12:12 PM

And dq = σdS

Opt•4/13/25, 12:12 PM

So that's a scalar

AetherflyOP•4/13/25, 12:12 PM

oh yeah

Opt•4/13/25, 12:13 PM

So your integral is ʃEσdS ?

Opt•4/13/25, 12:13 PM

The only vector in your integral is E, and that cancels out because each field line has one in the opposite direction

AetherflyOP•4/13/25, 12:13 PM

yup

AAetherfly Click to see attachment

AetherflyOP•4/13/25, 12:13 PM

how r we doing this

AetherflyOP•4/13/25, 12:14 PM

by the same logic E is the only vector here

AAetherfly by the same logic E is the only vector here

Opt•4/13/25, 12:14 PM

Ok, but there you don't have fields that cancel out.

Opt•4/13/25, 12:15 PM

And for that question too, try doing the Newton's third law method.

OOpt Ok, but there you don't have fields that cancel out.

AetherflyOP•4/13/25, 12:15 PM

but we're still writing EdScostheta = phi

AAetherfly but we're still writing EdScostheta = phi

Opt•4/13/25, 12:16 PM

Ok, so there's an abuse of notation going on there. Let me type in LaTex for you to understand better

Opt•4/13/25, 12:19 PM

It is correct up till

$\vec{dF} = \vec{E}\sigma dScos\theta$ and
$\vec{F} = \int\vec{E}\sigma dScos\theta$

However, converting that into flux neglects one point. It should be written as

$\vec{F} = \sigma\left(\int\vec{E}\cdot\vec{dS} \right)\hat{E}$

Where $\hat{E}$ is the unit vector in the direction of the field.