Gauss's Law Problem: Sphere and Conducting Shell

Physics Ninja looks at a classic Gauss's Law problem involving a sphere and a conducting shell. The inner sphere can be a conductor or an insulator and the outer shell is assumed to be a conductor. Charge is placed on both the sphere and shell. We use Gauss's Law to find the Electric Field everywhere in space.

[@calthar13]

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[@PhysicsNinja]

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University...., I'm learning this in 9th grade.

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[@mrtom-a-hawk6732]

Wow, this is a lot easier than my professor made it out to be. Thank you so much!

[@mohammadmaarefi3393]

Beautifully made, I love how you mention all possible cases of this question. It makes perfect sense.

[@PhysicsNinja]

Thank you so much!

[@aaronlopez3852]

This is awesome. Thanks for being thorough, yet concise. Keep it up!

[@farhanbinfaisal135]

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Watched you video and went back to what my professor did and it made a lot of sense to me. Thank you very much and I must say my professor teaches well too.

[@ice_the_kicker]

Brilliant explanation. I have never actually been into the world of physics, mostly programming and mathematics. Your video triggered me into learning electromagnetic fields.

[@PhysicsNinja]

Thanks you. Good luck with your studies.

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Wow... It's now that I understand this completely... Thank you.... 😊

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[@PhysicsNinja]

You got this!

[@jennaalqdah9538]

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[@PhysicsNinja]

Thank you so much. These types of comments motivate me to make more videos.

[@carsontaylor8771]

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[@kommsk]

You did a very good job explaining Gauss' Law through a real example...Thanks man , you're a Ninja...:)

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Excellent video! Made me understand Gauss's Law perfectly.

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Thank you so much!! I was so confused and now I solve for my upcoming mid exam.

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[@eccedentesiast4647]

Superb and amazing 👌🙌😍 explanation. Infinitely many thanks to you from my bottom of the heart.

[@MultiSubjector]

Thanks for the clear and concise lesson. I haven't seen this since taking physics, and revisiting the concept for one of upper div EE courses has been rough with my professor

[@PhysicsNinja]

thanks for the comment. I'm happy the video was helpful for you. Good luck with your course.

[@kabandajamir9844]

The world's best teacher

[@ironears]

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[@PhysicsNinja]

Glad it was helpful!

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[@faisalali2001]

Great work

[@THEVEGEfr]

Thanks for the helpful video sir!

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[@abdallahmohamed8167]

قمه الجمال والله و قمه الفهم ف 18 دقيقه بس
loved that 💛💛💛💛💛

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Online learning moment. So much simpler than my professor made it out to be.

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Tks nice explanation

[@batuyild]

Helpful..Thanks..

[@PhysicsNinja]

Most welcome!

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Thanks.

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beautiful

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You really saved me!

[@dilipmahalingam]

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[@archieli4556]

Thank you Sir!!!! I understand now！

[@REASON_REALM]

you are the best

[@FaridCenreng-]

Why the outer sphere dont affect in the white field (a

[@PhysicsNinja]

It’s only what’s on the inside that matters. If you would calculate the total fuel from outside shell you would find 0. It’s takes a bit of calculus to show but that’s also what you get from Gauss’ Law

[@faraday7879]

you are the man

[@sabrinanovayanti3395]

so helpful

[@hotroadcol4166]

todos te amamos

[@kina4288]

When we say a sphere, are we automatically talking about a hollow object or not? I know a spade is a spade but when it comes to shpere, is it solid or hollow becomes important. Also, if the central charged object is off centre ie not at the centre of the metal shell, how it will change the calculation? Thank you ninja

[@RAYAMUSTAFA]

can you please explain how you so easily plugged in 4/3pi r^3 / 4/3pi a^3?

[@nashhm7693]

If it is metal sphere. The r

[@PhysicsNinja]

Yes

[@markkennedy9767]

At 2:00 are you saying that the only way E=0 everywhere inside is if q_enclosed=0. I'm pretty sure that isn't true. As you know, the integral (which evaluates to q_enclosed) can be zero but the integrand E could be non-zero in places.
The implication the other way is true: if E=0 inside everywhere is zero, then q_enclosed is zero.
My question is:
Can you explain why in an electrostatic situation on a conducting sphere, that the electric field inside is zero necessarily. I know that in an electrostatic situation, the electric field has to be zero where the charges are (otherwise the charges would move), but why does the electric field have to be zero where the charges are not.
The usual explanation in texts is by contradiction: i.e. if we had an electrostatic arrangement and we were to place another charge inside the sphere it would move if the electric field was non-zero inside, supposedly contradicting the original electrostatic situation.
But by placing another charge inside the sphere aren't we changing the original electrostatic arrangement that we assumed. So we're not contradicting the original electrostatic arrangement. So it's not really a contradiction.
Can you tell me where I'm going wrong with this.
Thanks.

[@alzahraz]

thanksss!!!

[@amlhassan7090]

hi how can i calculate the surface charge density on the inner surface of the outer spherical conductor and on the outer surface of the outer spherical conductor?

[@Wave_equation.]

nice

[@slendermangaming6414]

I love you so much

[@MuhammadAli-tw9ht]

Sir , can i please know about the potential inside the shell? As electric field is zero inside shell , the potential will be constant but would it be same as due to inner sphere or the conducting shell.?

[@omercankilickaya9965]

If inner -Q and outside 3Q how is the solution change

[@andrewjustin256]

14:40 Would you, sir, clarify how the charge outside be positive when the charge is negative on the shell?

[@isaacverdeciacarrion145]

thanks

[@JB-tj2ot]

so if im asked to get the EF inside the sphere what would the answer be=(? 0?

[@philip-zr5my]

you are awsome
:3

[@omniamohamed404]

for region two, it is still inside the outer sphere which is conducting, so how is it possible that region two does not have zero electric field?

[@PhysicsNinja]

Because the is charge on the inner sphere

[@yuvanm359]

Tanks man

[@AngelaAngel-v6j]

It was awesome
But I have a doubt, what about at point b? I mean how to find E right at b point?

[@sudhanshub999]

See case 2 heading there clearly written that a

[@bshdjdjfnfjd8379]

I wonder why the electric field at r=a ( conducting sphere ) equals to zero🤔

[@ahmadirshaid6497]

Is the electric field on the outer shell when (r=c) is zero ????
and when (r= a) is zero too??

[@SADDAMHUSAIN-ly4mm]

S I am saddam husain from india . SirMy small talk with you is that you should solve more problems like this in the book of DavyJ Griffth by putting limit in electric field and solved more such problems sir please......and please reply sir

[@hazimaznan2077]

Tq for the video

[@Clintaso]

Any reason you didn't do an example in the case of an insulating shell? Is it just not common?

[@bautistabaiocchi-lora1339]

ty

[@liambrennan4902]

How would we find potential at the center of both spheres?

[@dakshigoel9543]

sir, if a=b then how will we find the electric field anywhere inside the spherical shell??

[@PhysicsNinja]

If a=b it looks like it would simply be a conducting sphere with radius c. E=0 inside conductors. The charge would be at the surface c.

[@harbinger9231]

Thanks a lot but how do you find the potential across two points in such a setup?

[@PhysicsNinja]

Delta V= -integral( E.dl)

[@Alidaher2468]

But for a conductor the electric field inside is zero and therefore in the case 2 the charge is zero

[@Alidaher2468]

Or the inside is dielectric?

[@jadenjohnson4850]

How would E change in the case of r being between b and c if the shell is an insulator?

[@PhysicsNinja]

If the charge is spread uniformly in the outer shell then you can still calculate using Gauss' Law. The field will be different!

[@walterdiaz2003]

Do licensed electrical contractors know this or should?. I know some physics 1/2/3, Digital Systems 1 and so on. I have a BS in Computer Science but I am interested in getting the plumbing and electrical licenses (Homeowner issues....). Any advise?

[@PhysicsNinja]

Absolutely not!

[@eraysona]

jesus. now I can show off the girls in my uni!

[@PhysicsNinja]

Chix will dig it.

[@ahmedalmoola8191]

good video but I hated the many ads poped and distracted me.

[@vikramnagarjuna3549]

Hi sir this is Vikram from India, please do some problems on coupled oscillators in SHM with simple mathematics or advanced Mathematical methods.

[@dawwnbrk3r653]

🐐

[@lawrencelam2333]

Best video ! ua-cam.com/video/pzJanh-Ol4g/v-deo.html Can we say (-1 Q ) charge distributed evenly in both inner and outer shell or just (-3Q)charge in inner shell and (+ 2Q) charge in outer shell.

[@efeturan3278]

so bad wroong

[@PhysicsNinja]

Lol

[@amlhassan7090]

hi how can i calculate the surface charge density on the inner surface of the outer spherical conductor and on the outer surface of the outer spherical conductor?

[@PhysicsNinja]

Total charge on that surface / (4*pi*R^2)
The term in denominator is the total surface area of the sphere.

[@amlhassan7090]

@@PhysicsNinja ok thanks

[@amlhassan7090]

@@PhysicsNinja is there is any chance / way that i can send you a question to help me with ?