In what direction does the sphere move between two positive charges

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The dielectric can be polarized. So you can also have surface charges, but instead of them being free, they are now bound. Then you will get a surface charge density much like the conductor but much smaller in magnitude.

EDIT: Very similar to a balloon that you statically charge then hold it near a wall. The wall is a dielectric and will be attracted to the charged balloon.
 
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