Electric field from a polarized metal sphere?

[txaggiechick]

First, there is a positive point charge sitting in space which creates an electric field around it. Then, a large metal sphere with no net charge is a added some distance to the left of it. Does the addition of this sphere change the magnitude of the electric field at some points a and b which are in between these two objects?


So I know that the large metal sphere will now be polarized but I am not sure if this polarization will have a force on this these spots or if it will cancel out since one side is negative and one side is positive

 

[AEM]

Suppose you replaced your sphere by two point charges, one positive and one negative (a dipole) with the negative charge of the dipole towards the given positive charge. How would you answer the question then? You'd just add up the vectors at your points a and b taking into account the distance of a and b from the three charges. The sphere problem is just a variation on this situation.