The potential difference between a sphere shell and a point

[Tomi Kolawole]

I am to use this formula:
https://d2vlcm61l7u1fs.cloudfront.net/media/fee/fee798ea-5480-47af-9904-35c76ac35e25/phpSzecLa.png

I tried using intergral of (E*dr) as in the equation to integrate over the distance of V(2A)-V(0) But when i am to plug in zero into my integrate it would give a math error in the form of 1/0 since my radius would be 1/r in the integral

 

[Buzz Bloom]

Hi Tomi:

What do you know about the potential inside of a thin shell of equally distributed charge per square unit of surface area?

What do you assume about the charge between radius r and r+dr with respect to the problem statement?

Regards,
Buzz

 

[Tomi Kolawole]

It says it has uniform charge of -Q all through out the sphere.So i assume that -Q is for my charge enclosed.Using Gauss law to formulate the expression for E.

Is the potential zero? I know the electric field is constant due to symetry but is the potential zero?

 

[Tomi Kolawole]

Why isn't the charge enclosed -Q, since the -Q will gather on the outside of the sphere with radius A

 

[Buzz Bloom]

Why isn't the charge enclosed -Q, since the -Q will gather on the outside of the sphere with radius A

Hi Tomi:

The question the problem is asking is not the charge put the potential.

To answer your question in the above quote, you need to think about making an assumption regarding the nature of the material the shell is made of. Is it a conducting material like a metal, or an insulating material mostly like a plastic?

Also, if it were a metal, where would the charge be located?

Regards,
Buzz

 

[Tomi Kolawole]

if i Assume its a conducting material, the charges can only be on the surface? Where would it be for an insulating material>

 

[Tomi Kolawole]

i think i have it the other way around,For an insulator the charge will be on the surface only and then for a conductor it will be all around it including within

 

[Buzz Bloom]

if i Assume its a conducting material, the charges can only be on the surface? Where would it be for an insulating material>

Hi Tomi:

Inner or outer surface of the shell?

Where would it be for an insulating material>

The original problem statement used the word "uniformly". Do you you are required to explain how that works? Or is it sufficient to just assume that it works?

Regards,
Buzz

 

[Tomi Kolawole]

since its unformly distrubuted will i need to find its charge density first?
But assuming they said there is a charge -q inside the sphere of radius A, in that case i can assume it an conductor? and then use -Q for my enclosed charged directly? but if its an insulator the charge would be distrubted on the surface of the material instead?

 

[Buzz Bloom]

i think i have it the other way around,For an insulator the charge will be on the surface only and then for a conductor it will be all around it including within

Hi Tomi:

A conductor is a material in which charges can move easily. That is why they are used to get electricity form one place to another. an insulator is a material in which charges do not move easily. That is why electric wiring has an insulator on the outside, so that someone touching the outside won't be shocked by the electricity running through the inside conductor.

Imagine someone inside a conducting shell with a source of static electricity, that is, charged particles. If the source touches a point on the the inside surface of the shell, where would the charges move to?

Regards,
Buzz

 

[Tomi Kolawole]

the charges would move everywhere around the conducting shell

 

[Tomi Kolawole]

no it would move to the surface of the conductor

 

[Buzz Bloom]

o it would move to the surface of the conductor

Hi Tomi:

Inside or outside surface?

Regards,
Buzz

 

[Tomi Kolawole]

outside surface

 

[Buzz Bloom]

since its unformly distrubuted will i need to find its charge density first?

Hi Tomi:

You might want to think about the quantity of charge from a radial perspective. That is, what fraction of the charge is between radius r₁ and r₂?

Regards,
Buzz

 

[Tomi Kolawole]

why is it that there is no charge inside the sphere of radius A? because to calculate the electric field from the centre to My gausian saurface between A AND 3A i will have to neglect the distance r<A during my integration.

 

[Buzz Bloom]

why is it that there is no charge inside the sphere of radius A?

Hi Tomi:

If there were charged particles inside the shell, how would they react to each other? Where would they end up? How would this affect the "uniformity" of the charge within the shell between R = A and 3A?

Regards,
Buzz

 

[Tomi Kolawole]

i figured it out and i got the right answer.except i have a -q instead of just a +q in the final answer equation.Is this because its an insulator so the sign of the charge doesn't matter?

 

[Tomi Kolawole]

also is the charge density of the entire sphere the same at any specific point of the same sphere? what conditions would make this true?

 

[Buzz Bloom]

i have a -q instead of just a +q in the final answer equation.Is this because its an insulator so the sign of the charge doesn't matter?

Hi Tomi:

http://farside.ph.utexas.edu/teaching/302l/lectures/node35.html
This article makes clear that the sign of the resulting potential from a charged source is the same sign as the source.

also is the charge density of the entire sphere the same at any specific point of the same sphere? what conditions would make this true?

That is what "uniformly" means.

i figured it out and i got the right answer.

Congratulations. Good work.

Regards,
Buzz