Qualitative Solid Spherical For a charged solid metal sphere with total charge Q
ID: 1406156 • Letter: Q
Question
Qualitative Solid Spherical
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 electric field for r << R would be the same as that of a conductor with the same shape and charge.
2.The electric field inside the solid metal sphere is never zero.
3.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.
4.The net charge on the inside of the solid metal sphere is negative.
5. 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 neutral.
6.The electric field near the metal surface on the outside is parallel to the surface.
*Gauss' Law states that the electric field inside a closed conductor is zero. The electric field must be perpendicular to the surface of a conductor.*
Explanation / Answer
Let's check one by one:
1. FALSE: If the sphere is made of insulator material, we could consider that the charge is uniformely distributed, and a sphere of radius r would close some charge but it is not the case for the metal sphere, since all its charge is on the surface (at radius R); therefore there is no charge and no electric field.
2. FALSE: the electric field is always zero inside a solid metal sphere, because all its charge is on the surface. According to Gauss law, since there is no closed charge, the electric field is zero.
3. FALSE: there is no charge inside the solid metal sphere, therefore there is no electric field inside a sphere of radius r.
4. FALSE: The charge is on the surface, there is no charge inside the sphere.
5. TRUE: but the charge Q must be placed at the surface of the sphere, if it is uniformely distributed, the net charge is not neutral.
6. TRUE: this is why the Gauss law is very useful for certain geometric shapes.