Charging metal spheres by induction

When a neutral object is charged by induction, the object is charged by the mutual repulsive forces that build up between the neutral object and the charged object, without establishing physical contact between them.

How is a neutral object charged using a charged object?

For example assume that there’s a neutral sphere and we bring a positive rod near this object. Now remind that an object being neutral is not that it does not have any charges in it. A neutral object is any object where the total no. of positive charges is equal to the total no. of negative charges.

As the charged rod approaches the neutral sphere, the negative charges on the sphere are attracted toward the rod and the positive charges are repelled. Note that the sphere is still neutral.

When the sphere is grounded by a wire, electrons move up from the earth and give the sphere a net negative charge.

When the ground wire is removed there are only negative charges in the sphere. This means that the sphere is entirely negatively charged.

When the charged rod is also removed, the negative charge is spread uniformly throughout the metal sphere (leaving no positive charges).

Now what happens when two such spheres are kept close to each other?

Consider two sphere systems set side by side.

When a negative charged rod is brought near one of the spheres, electrons in the sphere close to the rod will be induced to move away from the rod. Thus, the final distribution of the charges in the presence of the conductor will be as follows:

When both the second sphere is removed and the rod is taken away from the two systems, the final charge distribution of the two spheres are as follows (uniform charge distribution):

When a positive charged rod is brought near one of the spheres, a charge variation as follows can be seen:

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