Electrical Potential of a Conducting Sphere (or Shell)

Physics Ninja looks at the derivation of the electrical potential of a conducting sphere. The electrical potential is found for points outside the sphere as well as for points inside the sphere. In Part 1 evaluate the integral for the potential difference. In Part 2 I integrate of the surface charge density.

[@aksh08]

Thank you so much! This video was really helpful 🎉

[@abhijeetgaming8848]

Thanks sir

[@iloveanime-q6s]

Hey i asked a doubt on cart collision with a spring in a video you posted a year ago. Can you pls ans my question as to why do we not take momentum of spring in those numericals while we are taking momentum of carts

[@PhysicsNinja]

Good question. For most problems we assume the mass of the spring is negligible compared to the other masses. Therefore it’s momentum and kinetic energy will also negligible.

[@sarubet8725]

Wow you made this more complicated than it needed to be.

[@PhysicsNinja]

Sometimes if you just give someone the answer they might remember it for a day or a week but if you show someone where the answer comes from and how it can be obtained they will remember it for the rest of their lives. I’ve interviewed 100s of engineers who could answer simple questions related to the potential if charged shells because they only learned the answer for test in college.

[@giovannipiacen85]

There's something that is driving me nuts and can't find the answer of anywhere. Since delta V is the line integral of E dot dr from infinity to r, and we are moving against the electric field going from infinity to r (assuming a positive charge), E dot dr should be -kqdr/r^2, not kqdr/r^2, which leaves an extra minus sign which would make V negative at the end. I know it's not supposed to be, but I can't figure out the solution of this issue and I looked everywhere

[@PhysicsNinja]

This drove me nuts this semester too. You need to be extra careful with dr in this case. r is defined from the origin so dr will be negative.

[@aksh08]

Hey! I have a very silly doubt… what’s the difference between electric potential and electric potential difference?

[@PhysicsNinja]

@@aksh08 the integral equation always calculates the difference in electrical potential. Sometimes a reference point is defined for electrical potential like in this case. V=0 for a point very far away from the sphere.

[@aksh08]

@@PhysicsNinja got it! thanks

[@osgwow]

but if its shell there is no potential in inside why you said sphere or shell on title?

[@PhysicsNinja]

The potential is constant inside the shell. The electric field is 0.

[@osgwow]

@@PhysicsNinja we thought every shell is conductor?