Physics 38 Electrical Potential (12 of 22) Potential In-, On, & Outside a Spherical Conductor

[@drewpierpont3361]

Saved me when I took the course, saving me again now that I'm a supplemental instructor for it. Thank you so very much Sir.

[@panther7341]

bro in india 16 years old student who prepare for jee its just very very easy task to calculate

[@sandorfogassy3007]

Very thankful for your videos. Makes studying so much more efficient.

[@valeriereid2337]

Thank you Professor. You are the best at making these concepts easy to understand.

[@MichelvanBiezen]

Glad you like them!

[@mechanicfury]

Eyvallah reis hem Fizik hem İngilizce çalışmış oldum. Love from Turkey!

[@MichelvanBiezen]

Welcome to the channel!

[@mechanicfury]

@@MichelvanBiezen 🖐🏾❤️

[@elephant35e]

Way better than my Physics teacher. She does NOT teach at all.

[@iranpop80slover]

1:50 potential decreases as we go into distance therefor we put - ? doesn't the limit of r approaching infinity already make that happen ?

[@MichelvanBiezen]

Abtin, This is always a confusing topic. It simply comes from the definition of potential difference. A negative is required there for the answer to come out correctly. It does seem counter-intuitive, but that is how it is defined.

[@PrivacyKingdoms]

Michel van Biezen i am also confused by the negative. so all i need to know is that by definition v =-ed no matter what? I am trying to understand it intuitively but I can't.

[@LittleWaffle]

As always, you're very helpful and a blessing in times of finals, but not only. Thanks. Keep it up!

[@ribedon]

Thank you so much, sir, really needed to know what the potential would be inside the sphere.

[@MichelvanBiezen]

The potential inside the sphere will be the same (everywhere in the sphere) as the potential at the surface. Since the electric field inside the sphere is zero, the potential cannot change relative to the potential at the surface.

[@shafinahmed3753]

Michel van Biezen could you pls tell me why the electric field inside the sphere is zero and why the potential in the sphere is same as the surface.

[@rasangiejayalath180]

Shafin Ahmed E (electric field ) inside is proportional to the charge inside sphere as this is a conducting sphere charge is on outside and therefore q inside =0

[@dipace16]

@Riya Kothari coz charge are uniformly distributed on the surface of sphere

[@reemibrahim4847]

What if the charged spherical conducter is next to a point charge.. what will be the electric potential inside the conducter and on the surface?.. and thank you.

[@Ele-qh3xc]

If I may ask, what if the sphere was an insulator? Would the electric potential vary with proximity to center? Thank you.

[@lil_weasel219]

if it was an insulator there would be no electric field at all I believe kek for anyone wondering

[@diags_1109]

@@lil_weasel219 I was thinking the same thing

[@manuelab.1850]

Hi.Can you,please,tell me is there an electric potential in a hollow sphere?I know that in solid sphere potential is the same everywhere,but I don't understand how it works in a hollow sphere.Thank you. :)

[@yourstruly33]

Yaa its also inside a hollow sphere. Potential is defined for a point in space and has no relation to the presence of matter.

[@busetosuner]

I understand the surface but I couldn't understand the inside. Since Q=0 and E= 0 and V=Ed, doesn't that make the Vinside =0 as well? Btw, thank you for the videos!

[@MichelvanBiezen]

V inside is the same as V on the surface. Change in V = E d so if E is zero, V doesn't change

[@helloworld12321]

Sir could you tell me where is the video of inside non conducting sphere electric potential

[@drhf1214]

sir, so this is saying that the potential inside the sphere at any point there is the same as the potential of the sphere exactly at a radius on the surface? Is this because if dv = 0, there is no change therefore V is constant? What case would V be 0?

[@MichelvanBiezen]

That is because the electric field inside the sphere is zero and thus the potential cannot change inside the sphere.

[@JossinJax]

@@MichelvanBiezen I'm confused. If E is zero, wouldn't V be zero as well? I see you have explained it numerous times, but perhaps the difference between "potential difference" and "potential" is unclear. I am about to take my university physics 2 final and honestly still don't understand this concept.

[@hyunsuphan4747]

@jhopeful my guy had a whole tutoring session alone XDDD Thank you so much for this man, I had this exact same question after watching Viren's video!

[@hyunsuphan4747]

@jhopeful cheers my guy. Nobody appreciated you for this? jeez

[@alperturna4371]

Great video, great way of teaching... Thanks a lot!

[@melanieveliz4210]

This made things very clear for me. Thank you!

[@MichelvanBiezen]

Glad it was helpful!

[@BaljinderSingh-tf2sn]

Clean presentation and made it easy!!!!amazing👌👌👌👌

[@joelip4396]

Why is R on the surface of the sphere relative to the center? Isn't the charge right where the point is (I know it's wrong, but I can't quite get straight in my head why r is not zero on the shell)? Does it just sort of average to a point in the center because of the distances to the charge on the other parts of the sphere?

[@MichelvanBiezen]

R is the radius of a circle and it is always measured from the center of the circle.

[@weamhaleemi4984]

You say the method.. please explain it.. why is it like that

[@asmatawan8922]

Measure the surface charge density at some point say ‘P’ of an insulated conducting sphere, kept near a point charge. Please solve this question

[@boboganbobogan9297]

Is not the angle between the electric field vector and the dr vector equal to 180 degrees as we move from infinity to the point of interest?

[@MichelvanBiezen]

The potential energy is proportional to the electrical potential energy, which is obtained by performing a dot product with the force required to push the charge towards the sphere and the displacement, which are in the same direction.

[@boboganbobogan9297]

@@MichelvanBiezen In this case it is a positively charged sphere for which electric field lines point outward. When we go from infinity towards some distance r, do now we move opposite of the field lines?

[@MichelvanBiezen]

In this case the direction of the electric field lines are not relevant. Only the direction of the force pushing the charge and the direction of the displacement. The electric field lines do point away from positive charge.

[@boboganbobogan9297]

@@MichelvanBiezen okay, thank you

[@numbo655]

Assume the sphere is thick, and so has a volume charge density. What would be the potential inside the "membrane" ?

[@MichelvanBiezen]

I believe we have videos on that as well in the playlist.

[@iliaskarimi9817]

Hi sir, i need help for Gauss's method when we calculate the electric field (out of sphere) why the distance is from the center, why not from the surface because the charges is in the surface not in center and thank you very much

[@MichelvanBiezen]

Using Gauss's law it can be shown that the electric field outside the sphere is as if all of the charge is located at the center.

[@iliaskarimi9817]

How that please ? give me PDF or document about this please ... i'm very confused

[@TheOlly95]

I dont understand the negative sign. if R goes to infinity the Potential decreases down to zero at most. Why negative

[@MichelvanBiezen]

+TheOlly95 There is no such thing as an absolute potential value. Potential is referenced to a reference value. For example we arbitrarily set potential to zero at infinity and then compare the potential to that value and that location, everywhere else. And thus only the difference in potential matters.

[@minhvule1608]

I have never said this before but... I love your videos so much ( wanna cry 🤣🤣🤣 ), thanks so much 👏👏👏

[@duykhanh7746]

chị ơi chị giải thích cho em phần inside đc ko ạ :( tại sao E=0 thì V lại bằng nhau ở mọi điểm ạ

[@minhvule1608]

@@duykhanh7746 đạo hàm á e, E là đạo hàm của V theo r.Nếu E=0 tức là đạo hàm của V theo r bằng 0, mà chỉ có hằng số mới đạo hàm ra 0.Như vậy V bằng nhau ở mọi điểm

[@minhvule1608]

@@duykhanh7746 em đg học đội tuyển hả, c nghỉ cg 1 năm rồi nên k bt giải thích có sai chỗ nào k 😅😅😅

[@duykhanh7746]

@@minhvule1608 e cảm ơn chị ạ. E đang học lý 2 mà thấy sách giải thích chỗ này khó hiểu quá :(

[@MØDØK-007]

@@duykhanh7746 which language??🙄

[@FaridCenreng-]

I still don't understand. Why we need to integral it from r to infinity?

[@MichelvanBiezen]

The reference point of zero potential energy and therefore zero potential is at infinity

[@ahmethamdicelik1277]

How can we find electric potential inside and outside of a "insulated" sphere with given charge denstiy? How can we find electric potential if we have already calculated the electric field?

[@Aryan_editK]

Thank you, sir.🥰 Love from India.

[@MichelvanBiezen]

Welcome to the channel!

[@azzamqureshi2861]

If there is a cavity inside the sphere, the potential inside the sphere would still be the same, right?

[@MichelvanBiezen]

The potential can only change if there is an electric field: delta V = E * d If E is zero, the potential will not change.

[@BlueUKLouis]

Why is it the same though, it seems that multiply zero to a distance d would equal zero for V, I don't understand.

[@Ele-qh3xc]

maybe cause it is delta v = E *d, as in change in V. In which case, since inside sphere (if no charge exists inside cavity) electric field is 0, 0 *d = 0 change in delta V, but not V

[@CatsBirds2010]

Graphing always helps me understand better and thanks.

[@spurti]

Hii I have a question why the electric field is zero inside the conducting sphere??

[@MichelvanBiezen]

All of the charges will reside on the surface of the conductor since they repel each other, so they can be as far away from one another as possible. Electric field emanates from positive charges and terminate at negative charges. Since there are no negative charges inside the conductor, no electric field lines will be directed inside the conductor.

[@spurti]

@@MichelvanBiezen thanks for the explanation!!

[@cristyhagi1987]

can u explain why there is dv in voltage sir?

[@cristyhagi1987]

answer please thank you :D

[@MichelvanBiezen]

You may want to watch these videos first to get a fundamental understanding of "voltage" first. Then we can tackle your question here. See the playlist: PHYSICS 38.1 VOLTAGE UNDERSTOOD

[@cristyhagi1987]

@@MichelvanBiezen i did, dv because EM is not constant, isn't it?

[@MichelvanBiezen]

That is correct. I wasn't sure about your question, but now I understand you were asking why dV instead of delta V.

[@rahultiwari9003]

Sir in case of a spherically charged insulator what will be the potential at the centre.I tried this by taking the integral of E=p(rho)r/3€ and the limits as 0 to R but I am not getting the correct answer.Where am I going wrong sir ??

[@deepjyotisaikia2127]

Why the distance of charge to the point outside is measured from the centre why not from the surface Pls explain..

[@MichelvanBiezen]

Since all the charge is placed on the surface of a sphere, the symmetry of the physical setup can only be utilized if the position for which the electric field or potential needs to be calculated must be referenced to the center of the circle. In this way it doesn't matter which point you pick, it is valid for all points inside or outside the sphere.

[@khaileng3020]

If we use the work done to calculate potential by V=w/q, is it hard to do that ? I am very confused when to use work , and when to use electric field ,to calculate voltage

[@MichelvanBiezen]

You can use the first equation when there is a point charge. But when you have a charge distribution, it is better to use the electric field.

[@김상우-l7e]

Sir, would the answer be a negative if either the charge would be a negative or tje work done by the field be a negative?

[@MS-oy4vo]

Awesome explanation, thanks bro

[@minhvule1608]

At first, I thought that if inside the sphere E=0 then V=0??? Am I misunderstand something?

[@MichelvanBiezen]

Inside E = 0 but V will be constant and the same as what it is on the surface.

[@minhvule1608]

@@MichelvanBiezen thank you

[@taladiv3415]

I can't seem to grasp the connection between the mathematic formula and the assertion that V doesn't change when E = 0 . Plugging 0 in to the formula wouldn't give me V = 0 .

[@MichelvanBiezen]

The concept of voltage and the relationship to the electric field is fully explained in these 2 playlists: PHYSICS 38.1 VOLTAGE UNDERSTOOD and PHYSICS 38 ELECTRICAL POTENTIAL

[@taladiv3415]

@@MichelvanBiezen Thanks for the referral. I hope that I'll be able to make sense of this plot-hole there.

[@ther701]

This is gold.

[@RiyaTomar-jd3mw]

Professor, if inside the sphere E is 0, so if we put it in the equation dV=E.dr , mathematically shouldn't V also be zero? EDIT: I read the comments below, got a fair idea but still cannot get it that mathematically if we put E=0 in the equation it provides us with V=0. EDIT2: GOT THE ANSWER. I got that it was not V in the eqn., but it was dV so technically its CHANGE IN POTENTIAL DIFFERENCE and this is what exactly you said.

[@MichelvanBiezen]

dV = 0, which means that the voltage doesn't CHANGE inside the sphere, but the voltage inside will be the same as the voltage at the surface

[@RiyaTomar-jd3mw]

@@MichelvanBiezen yeah :)

[@oguzhanserce4480]

why we use the minus on dV?

[@MichelvanBiezen]

When dealing with potential difference it is often easier to realize that the potential decreases when moving from a high potential to a low potential and increases when moving from a low potential to a high potential. Only the difference matters, not the actual voltage.

[@syahadatulhidayat1325]

Why don't we just calculate the Potential by finding the Electric Field at r by gaussian method and then multyply it by r?

[@MichelvanBiezen]

+Syahadatul Hidayat Why don't you try it and see if you get the same answer? That is a good way to learn.

[@syahadatulhidayat1325]

Thank you my good sir

[@sibesokalaluka2991]

Thank you so much. You make it easier 😊

[@saraskenderaj5543]

how can we find the total charge on the surface of the sphere??

[@MichelvanBiezen]

That depends on what is given. If you are told the strength of the electric field at some distance then you can use Gauss's law. If you are told the surface charge density you can multiple the density with the surface area. If the charge density varies with position, then you'll need to integrate. If you are given the potential at some distance then you can find the electric field and then use Gauss's law.

[@lapertica8258]

Great like always. Thank you Professor

[@diyaael-shorbagy7056]

how can we drive the equation inside if the sphere was insulating ?

[@MichelvanBiezen]

There some examples like that in the 2 playlists. Here is one: Physics - E&M: Ch 37.1 Gauss''s Law Understood (18 of 29) Spherical Insulator

[@ongoingcajourney9938]

Amazing explanation sir 😊😊😊😊I am from India than also understanded very nicely 🤗🤗🤗😀😀😀lots of love from India

[@MichelvanBiezen]

Welcome to the channel!

[@dipace16]

why potential is not zero inside the sphere even if electric field intensity E=0 as V=E.d !!!!?????

[@MichelvanBiezen]

The potential inside the sphere doesn't CHANGE and since it doesn't change it will have the same value as on the surface.

[@dipace16]

If E=0 then according to V=E.d V should be zero no!??

[@MichelvanBiezen]

Only if the potential is zero at the surface. Note that the CHANGE in potential = E x d

[@MuhammadIrfan-ko5rr]

Sir ,what would be the potential out side an arbitrary shape

[@BeerJxx]

the way you put the minuses always confuses me so much. i watched many videos on this channel, and those minuses are so confusing to me.

[@tand9854]

The minus sign just shows that E acts in the direction of higher to lower potential

[@gitgud431]

How do you find its potential energy?

[@MichelvanBiezen]

See the other videos in the playlist that explain that topic.

[@gitgud431]

@@MichelvanBiezen Got it. Thanks!

[@rameshseth9096]

Very helpful. Thankyou !

[@MichelvanBiezen]

Glad it was helpful! 🙂

[@MannuKumar-wk4kx]

Thanks a lot sir😚

[@MichelvanBiezen]

Most welcome

[@danielafilipovic1685]

what about an insulator?

[@MichelvanBiezen]

+Daniela Filipovic Take a look at this playlist. There are lots of examples with insulators to help you understand the relationship between the electric field and the potential. PHYSICS 39 CAPACITORS

[@LittleWaffle]

Michel van Biezen thank you very much!

[@MohamedMostafa-jq8rl]

sir i don't understand why integrating with respect to infinity ?

[@MichelvanBiezen]

+mohamed mostafa The potential is zero at infinity, therefore we must integrate from infinity to the point of interest.

[@sarahkenney5921]

Thank You!!! This was so simple.

[@PHYSICSGuna]

excellent sir thank you

[@MichelvanBiezen]

Most welcome

[@jserink1]

These are great videos except for this use of the nefarious "k". The use of the proper 1/4πε gives the student a feel, especially with the E field, that we're talking about the surface area of a sphere. Hiding this under some 'magic' constant 'k' masks this very important physical realization that many students miss. Cheers, Jim

[@nassimoumessoud8627]

Great explanation!

[@isha5999]

Thanks a lot sir, outstanding explanation.

[@baharerkut9535]

thank you so much

[@MichelvanBiezen]

You're welcome!

[@homodeus3820]

Excellent

[@MichelvanBiezen]

Thanks

[@supoyu6893]

thanks a lot

[@leylasolmaz3978]

pot difference is zero inside a conductor am i wrong sir? and also it has electric potential like kq/r but inside a conductor every value is same so it is zero. if am not true, please corrrect me sir

[@MichelvanBiezen]

leyla watson Leyla, The electric field is zero inside a conductor. But the potential is not zero.

[@leylasolmaz3978]

okey potential diffence is zero inside a conductor isnt it sir ?

[@MichelvanBiezen]

leyla watson Since the electric field is zero, the potential cannot change. Thus the potential DIFFERENCE must be zero between two points in the sphere.

[@leylasolmaz3978]

okey thank you very much

[@douniakabakibo8619]

+Burak Şahin well you need to look at this as an integral. Let's consider that the potential inside is Vb. Now we know that Vb-Va= -integral from b to a of E.ds where E (electric field)and ds (displacement) are both vectors. If you try to integrate between your position inside the conductor and infinity (in this case Va is at infinity =0) it would be difficult to calculate the potential because the electric field is not constant between these two points. Now try to integrate between your position inside the conductor and the surface of the conductor( in this case Va is at the surface and it is easy to calculate) You will have a potential that is equal to the one on the surface :Vb= -integral from b to a of E.ds +Va but E=0 so you have Vb=Va. I'm a student so maybe my analysis is not 100%right. Anyway hope it was helpful!

[@ElifArslan-l9g]

thank you

[@MichelvanBiezen]

You're welcome

[@sandeepparmar8767]

Please drive mathematically the potential inside the spherical conductor.

[@MichelvanBiezen]

Note that voltage is always expressed in terms of the "difference in potential", and thus must always be referenced to some point. Then also note that the voltage changes only when there is an electric field. If there is no electric field inside the sphere then the voltage cannot change anywhere inside the sphere.

[@sandeepparmar8767]

@@MichelvanBiezen okay sir, but how do we know that the constant potential inside the sphere is same as the potential at the surface ? Can we get it mathematically ?

[@MichelvanBiezen]

Delta V = E d Since E = 0 inside the sphere, V must be constant everywhere inside the sphere.

[@RiyaTomar-jd3mw]

@@MichelvanBiezen Voltage will change in the presence of electric field only if we move from one point to other, right?

[@abassopeyemi193]

i thought E=Kqq/r^2 ?

[@MichelvanBiezen]

That equation is used to calculate the force between 2 charges (Coulomb's law).

[@vishal_26641]

Only one who shows what he done in video on thumbnail.👌👌

[@ABHIJEETKUMAR-sx1kz]

Here E and dr are at dot product. So,we have toh take the angle also

[@MichelvanBiezen]

In this example the direction of the electric field and the direction of the displacement (dr) are the same and therefore the angle between them is zero. cos(zero) = 1

[@seaofpotions9877]

Thank you so much!

[@jaswanthreddy-jk1bq]

thankful

[@MichelvanBiezen]

You are welcome. Glad you found our videos. 🙂

[@aimanickel9680]

what is the electric potential in the center of the sphere?

[@MichelvanBiezen]

Then same as it is at the surface of the sphere. Since there is no electric field inside the sphere, the potential doesn't change.

[@mariaalzarooni3995]

very helpful... thank u

[@BufferOverflow_RSA]

uyindoda😎😎😎....

[@salmasiddiqui6560]

Why here E= v/d in the relation of E and V V/d has negative sign

[@MichelvanBiezen]

Voltage decreases when traveling farther away from a positive charge. Electric field decreases when traveling farther away from a positive charge.

[@khanhlinhdothi9625]

Thank you so much sir.

[@gourabhore4381]

Thanks

[@MichelvanBiezen]

Welcome

[@sharmilatudu3699]

Thank you sir

[@musiclab7696]

Thank you very much sir, very imformative and easy to follow and understand...been looking for this all day haha thank you again XD

[@danielvanderstruis1516]

Legend!

[@edwarddowling2119]

edward drowling

[@user-qg9ft4cp5p]

niceeeeeeeeee,is so clearly

[@yumvnit]

sir its an solid sphere

[@MichelvanBiezen]

Since it is a conductor it makes no difference if the sphere is solid or hollow. All the extra charge will reside on the outside surface.

[@tanyatanteta1801]

Life saver〒_〒

[@MichelvanBiezen]

Glad it was helpful. 🙂

[@noshinkhan5186]

👏👏👏👏👏👏👏👏👏

[@achyuttamrajtiwari3849]

You look cute in bow

[@Zmunk19]

your r's look like 2's