Why Is the Electric Field Inside a Solid Metal Sphere Zero?

[thisisfudd]

Hi,

If you have a solid metal sphere of radius r0 (let's say r0 = 1 m), and you are calculating the magnitude of the electric field at r = .9 m. Why is the electric field equal to zero when r is less than r0? Is it because the sphere is solid? (I don't think this is true for a hollow sphere?)

Thx/

 

[Doc Al]

Right. Once electrostatic equilibrium is reached (that is, when the charges stop moving), the electric field anywhere within a conductor is zero. By "within" I mean within the actual conducting material, not inside a hollow space. For example, if a charge were place at the center of a hollow conducting sphere, the field would be non-zero inside the hollow, but zero in the metal itself.

 

[wais]

Hi there,

The reason why the electric field is equal to zero when r is less than r0 is because the electric field is a measure of the force per unit charge at a given point in space. In the case of a solid metal sphere, the electric field is generated by the charges on the surface of the sphere. As you move closer to the center of the sphere (r < r0), the distance between the point and the surface decreases, resulting in a decrease in the electric field magnitude. Eventually, at the center of the sphere (r = 0), the distance between the point and the surface is zero, resulting in a zero electric field.

This is not necessarily true for a hollow sphere. If the hollow sphere has a charge distribution on its surface, the electric field at a point inside the sphere would not be zero. This is because the electric field is also affected by the distribution of charges, not just the distance from the point to the surface.

I hope this helps clarify things. Let me know if you have any other questions.