Why there is no electric field outside of the sphere

[brad sue]

Hi, I need to understand something:

A point charge -q is fixed at the center of a hollw spherical conductor of charge +q. Draw the electric field lines both inside and outside.

Please can you explain me why there is no electric field outside the sphere?
thank you

 

[jamesrc]

If you're using Gauss' law to find the electric field, then the total electric flux out of your gaussian surface is proportional to the enclosed charge. If you add up the charge inside your gaussian surface (say, a sphere with a radius bigger than the spherical conductor), what is it? (what is -q + +q?)

 

[quicknote]

There are a few reasons why there is no electric field outside of the sphere in this scenario.

Firstly, the electric field lines outside of the sphere would be perpendicular to the surface of the sphere. This is because the electric field lines always point in the direction of the electric force, and the electric force on a test charge outside of the sphere would be directed towards the center of the sphere due to the presence of the fixed point charge at the center.

Secondly, the presence of the conductor itself also plays a role. Conductors have free electrons that can move around and redistribute themselves in response to an external electric field. This redistribution of charge creates an opposing electric field that cancels out the external field. In the case of a hollow spherical conductor, the free electrons will distribute themselves on the outer surface, creating an opposing electric field that cancels out the external field.

Finally, the electric field inside of the hollow spherical conductor is also zero. This is because the free electrons on the inner surface of the conductor will redistribute themselves in such a way that the electric field inside is also canceled out. This is known as the "Faraday cage" effect.

In summary, the combination of the electric force from the fixed point charge and the opposing electric fields from the conductor result in a net electric field of zero outside of the sphere. This is why there is no electric field outside of the sphere in this scenario.