You have a neutral soda can and a positively charged object. You bring the positive object near, but do not touch the soda can. No sparks occur. While you are doing this and before you remove the positively charged object, what is the charge on the whole soda can?

Question - What happens when you rub a balloon with wool and hold it next to an object that is neutral?

1. All objects, even those that are "neutral," are composed of many particles that are electrically charged. When they are neutral, the amounts of positive and negative charges are equal to each other, and they are closely mixed together.

2. The force of electric attraction or repulsion gets weaker as you move the charged objects apart.

When an object with a net electric charge is brought near an object with zero net charge, the smaller charges making up the neutral object become polarized. Let us say that the charged object has a positive charge. Then the negative charges in the uncharged object will be attracted to it and the positive charges in the uncharged object will be repelled from it. So, the uncharged object will have a slight negative charge on the side near the positively-charged object, and a slight positive charge on the side opposite the positively-charged object. (The more easily that charges can move in the uncharged object, the more complete this polarization will be. Try bringing your charged balloon near an empty aluminum soda can lying on its side. The aluminum is a good conductor, so charges polarize within it easily, and you can get the can to roll toward the balloon.)

Because the electric force is stronger at close distances and weaker at long distances, the positively-charged object will attract the nearby negative charges in the neutral object more strongly than it will repel the more distant positive charges. So, the net force will be an attraction.

https://www.physicsclassroom.com/class/estatics/Lesson-1/Polarization

If you do not touch the can, it will remain uncharged, or neutral. It will be attracted to the charged object because of the separation of charge within the metal, as described by zbeckabee, but will not have any overall charge as long as it is electrically isolated.

However, if you touch the can, or provide another path for charge to move to or from the can, then it will become charged. This is called charging by induction. If the charged object is positive, it is attracting the mobile electrons towards itself, leaving the fat side of the can with an excess of positive charge. If you touch it or earth it, extra electrons will flow through to the area of positive charge. Remove the contact, and the can will be left with an overall negative charge. (If you hold a negative charge near, the final result is an overall positive charge.)

https://en.wikipedia.org/wiki/Electrostatic_induction