suppose you place a charge q near a large metal plate. (a) if q is attracted to the plate, is the plate necessarily charged? (b) if q is repelled by the plate, is the plate necessarily charged?

Electrostatics studies the forces between charged particles, finding that charges of the same sign repel and charges of the opposite sign attract.

Materials can be classified according to their charges mobility into two types:

Insulating. They are materials where the charges are fixed, therefore if you gain or lose charges the others cannot move.

Conductors. They are materials where the charges are mobile, if they lose charges the other charges can move to distribute the excess and or deficiency.

a) Indicate that we bring a charge close to a metal plate and it is attracted.

Because the plate is metallic, it has mobile charges.

The charge repels the charges of the same sign that are in the vicinity of it and there is a plate a excess of the opposite sign charges, therefore the plate attracts the charge, when removing the charge the plate remains neutral.

Therefore, for the plate to be attracted, it does not necessarily have to be charged.

b) Indicates that the charge is repelled to the metal plate.

This implies that there are excess charges on the plate of the same sign as the charge on the sphere.

When the sphere approaches, it repels charge of the same sign, therefore the charge plate decreases, but for there to be repulsion force the plate must be initially charged.

In conclusion, using the characteristics of electrostatics we can find the results for the attraction of the charge by a metal plate are:

a) The plate has no initial charge.

b) The plate has an initial charge.

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