Question

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.

Answer 1

The electric fields around charged solid spheres depend on whether the material is a conductor or insulator. Inside a metallic sphere, the electric field is zero, and on its surface, the field is perpendicular to the surface. Charge distribution differs between insulators and conductors.

Step-by-step explanation:

When dealing with a charged solid metal sphere, it's important to understand the behavior of electric fields in and around conductors. Let's evaluate the given statements step by step:

1. False: If the solid sphere is an insulator with net charge Q, the net charge on the inside is not necessarily negative. The charge can be distributed throughout the volume of the insulator.
2. False: For an insulator with net charge Q and for r << R, the electric field would generally not be the same as that of a conductor since the charges in an insulator do not need to be on the surface and can be distributed throughout the volume.
3. False: The electric field inside a solid metal sphere is zero. This is because the charges distribute themselves on the surface of a conductor, resulting in no net electric field inside.
4. True: The electric field near the metal surface on the outside is indeed perpendicular to the surface, due to the spherical symmetry and nature of the charge distribution on a conductor.
5. True: The electric field for r << R will be the same as the field of a point charge Q at the origin, as the charges on the metal sphere are at the surface, making the field the same as if the charge were at the center for points outside the sphere.
6. True: The net charge on the inside of the solid metal sphere is neutral since the charges reside only on the surface.

Answer 2

4 and 6 are true

Step-by-step explanation:

Let's analyze we use Gauss's law every situation presented

R1. False The sphere is insulating, so the entire charge is evenly distributed throughout the volume, but the sign of the charge does not change.

R2. False In a conductor the entire charge is on the surface, therefore the electric field inside is zero, in an insulating sphere the electric field as the charge is distributed the field is proportional to the charge inside the Gaussian surface

R.3. False in a metallic sphere the charge is on the surface, by gauss law, inside it there is no charge, or therefore there is no electric field

R4 True. The electric field is as if all the charge were at the origin and the field lines have the same direction of the radii of the sphere that are perpendicular to the surface

R5 False In a metallic sphere the entire charge is on the surface, so the field is zero inside, instead a point charge has a non-zero field

R6 True. The load is on the surface