A mobile postive point charge is located between two parallel charged plates of charge densitys +o (top plate) and -o (bottom plate) at a distance d from the negative plate.the distance doubles (becomes 2d)between the negative (bottom) plate and the mobile charge...
will the magnitude of the electric charge become 1/4 of the initial value? or does it change in a different way?
To determine how the magnitude of the electric charge changes when the distance between the negative plate and the mobile charge doubles, we need to consider the electric field created by the charged plates.
The electric field between two parallel plates with uniform charge density can be considered as uniform. The electric field between the plates is directed from the positive plate to the negative plate. Let's call this electric field magnitude E.
Now, let's analyze how the electric field magnitude changes when the distance between the negative plate and the mobile charge doubles from d to 2d.
The electric field due to a point charge decreases inversely with the square of the distance. Therefore, when the distance is doubled, the electric field at the new position of the mobile charge will be (1/2)^2 = 1/4 times the original electric field E.
Since the electric field at the new position of the mobile charge is 1/4 times the original electric field, the magnitude of the electric force experienced by the mobile charge will also become 1/4 times its initial value.
Now, let's consider the force experienced by the mobile charge. The electric force experienced by a point charge in an electric field is given by F = qE, where q is the charge and E is the electric field.
Since the force is directly proportional to both charge and electric field, and the electric field becomes 1/4 times its initial value, the force experienced by the mobile charge at the new position will also be 1/4 times its initial value.
Therefore, the magnitude of the electric charge does not change when the distance between the negative plate and the mobile charge doubles. The magnitude of the electric charge remains the same regardless of the change in distance between the plates.