Qualitative Solid Spherical Conceptual

[roxnascarf9]

Homework Statement

For a charged solid metal sphere with total charge Q and radius R centered on the origin: Select "True" or "False" for each statement:

1.If the solid sphere is an insulator (instead of metal) with net charge Q, the net charge on the inside of the solid sphere is negative.
2. If the solid sphere is an insulator (instead of metal) with net charge Q, the electric field for r << R would be the same as that of a conductor with the same shape and charge.
3. The electric field inside the solid metal sphere is never zero.
4. The electric field near the metal surface on the outside is perpendicular to the surface.
5. The electric field for the metal sphere at r << R will be the same as the field of a point charge, Q, at the origin.
6. The net charge on the inside of the solid metal sphere is neutral.

Homework Equations

Gauss's Law: Qinside/ esub0

The Attempt at a Solution

1. False I'm not quite sure on this one

2. True I'm not quite sure on this one

3. False I;m not quite sue on this one

4. False, On the inside of a sphere the electric field is prependicular to the surface, but on the outside it wouldn't be

5. False I'm not quite sure on this one

6. True This is true becasue the net charge would be zero if the the eletric field is perpendicular.

 

[Simon Bridge]

Please show your reasoning for each of these so we can address your misunderstandings at their cause.
What leads you to suggest these answers - you don't have to be sure or even correct.

 

[Bhumble]

Welcome to PF. You should state your reasoning and not just true or false so that people can see where you are having issues.

1. Being an insulator or metal should impact the electric permittivity but shouldn't change the charge.

2. It states that they have the same shape and charge but I THINK an ideal conductor has all the charge on the surface. You should look it up to double check.

3. Answer to part 2 tells you this answer.

4. How is the electric field perpendicular inside and not outside? Imagine the inside and outside of a shell, what's the difference in angle?

5. Back to part 2. Unless this is suppose to be r>>R...

6. Depends on the characteristics of an ideal conductor. I'm pretty sure that the charge is all on the surface.

 

[Simon Bridge]

Welcome to PF. You should state your reasoning and not just true or false so that people can see where you are having issues.

Lets let OP tell us the reasoning before providing answers ;) this is homework after all.

Guiding questions (let OP answer):

1. Being an insulator or metal should impact the electric permittivity but shouldn't change the charge.

But how come? Can we think of any way to get extra positive charges into a neutral insulator? Is there any way the insulator will adjust so the net charge ends up negative?

2. It states that they have the same shape and charge but I THINK an ideal conductor has all the charge on the surface. You should look it up to double check.

OR, reason it out ... what is different between a conductor and an insulator, in terms of how charges move? How will the charges affect each other?

3. Answer to part 2 tells you this answer.

Not quite ... but this part must be false if any part of the inside has a zero field ever ... so if there are exactly two equal charges on the conductor - #2 tells you where they must be. From there you can see if there is any place where the field cancels out: you don't need the general rule but that is what they are aiming for and it's easier to remember.

4. How is the electric field perpendicular inside and not outside? Imagine the inside and outside of a shell, what's the difference in angle?

Note: the question is for r close to the outside ... if you are close enough to see individual charges, the sphere looks flat. How are these charges distributed? Sketch the field lines between these charges. Are they parallel?

5. Back to part 2. Unless this is suppose to be r>>R...

:)

6. Depends on the characteristics of an ideal conductor. I'm pretty sure that the charge is all on the surface.

Are there any charged particles inside a solid metal?

 

[Nickie]

I would like to clarify and explain the statements in order to provide a more accurate response.

1. False - The net charge on the inside of a solid sphere, whether it is an insulator or a metal, will always be positive. This is because the electric field lines inside the sphere will always point towards the center, regardless of the material.

2. True - For r << R, the electric field inside the sphere is primarily determined by the charge distribution on the surface, which is the same for both insulators and conductors. Therefore, the electric field for an insulating sphere with net charge Q would be the same as that of a conducting sphere with the same net charge and shape.

3. True - According to Gauss's Law, the electric field inside a solid sphere is given by E = Qinside/4πε0r^2, where Qinside is the net charge inside the sphere. As long as Qinside is non-zero, the electric field inside the sphere will also be non-zero.

4. True - On the outside of a metal sphere, the electric field will always be perpendicular to the surface. This is because the charges on the surface will redistribute to cancel out any electric field components that are parallel to the surface.

5. False - The electric field for a solid sphere at r << R will not be the same as the field of a point charge Q at the origin. This is because a solid sphere has a finite size and charge distribution, while a point charge is an idealized concept with all of its charge concentrated at a single point.

6. True - As mentioned in statement 3, the net charge on the inside of a solid metal sphere will always be neutral. This is due to the redistribution of charges on the surface, which will result in a cancellation of any net charge inside the sphere.