# Electric fields and a spherical surface

## Main Question or Discussion Point

If there's a point charge Q at the center of a spherical surface(of radius a) made of conducting material that is connected to earth, why is the electric field past r>a zero ?

Doesn't it imply that the spherical surface becomes charged with -Q ? And why is that?

What would be the difference if the spherical surface wasn't connected to the earth ?

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Simon Bridge
Homework Helper
A neutral objects contains an even mix of both positive and negative charge.
What does the central charge do to those mixed charges in the shell (assume the shell is not earthed to start with)?

When a conductor is earthed, any excess charge free to move will be drained away.

I would say that the surface becomes polarized ( -charges at the inner side and +charges at the outer side), that would make no difference to the electric field outside the surface, however, when the surface is connected to earth, the electric field outside becomes zero. Does that means that the +charges in the surface are drained away because they are being repelled by the center charge, and the -charges stay because they are being attracted ?

I said that the surface becomes polarized but since it's a surface it has no thickness,i.e:charges can't really be placed on the inner side or outer side. So if there was no connection to earth how would the charges on the surface place them self?

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Simon Bridge
Homework Helper
There is no such thing as zero thickness - that is an idealization.
If you like, you can think of the charges being pulled to positions infinitesimally just inside and outside the sphere.

There is no such thing as zero thickness - that is an idealization.
If you like, you can think of the charges being pulled to positions infinitesimally just inside and outside the sphere.

One last question, we assumed that the surface got charged with -Q. Is that value calculated by any equation? If so, what equations can I use?

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Simon Bridge
Homework Helper
Gausses Law.

Find the surface charge that makes the electric field inside the conducting shell zero.

I just read about electrostatic induction and it seems that the induced charge as the same value as the inducting charge, but with opposite sign.