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?
how can charge change?
will the magnitude of the electric field change*****
No. Neglecting fringing about the plates (assume they are infinite in direction), E is determined by charge alone.
E between parallel plates= areachargedensity/epsilion
To determine how the magnitude of the electric charge changes in this scenario, we need to consider the electric field between the two plates and how it affects the mobile charge.
Let's first define some variables:
- q: magnitude of the mobile charge
- E: electric field between the two plates
- σ: charge density (in this case, it is given as +o for the top plate and -o for the bottom plate)
- d: original distance between the mobile charge and the negative plate
- 2d: double the distance between the mobile charge and the negative plate
We know that the electric field between the plates is constant, given by:
E = σ / (2ε₀)
where ε₀ is the permittivity of free space.
When the mobile charge is at a distance d from the negative plate, it experiences an electric force due to the electric field. This force can be expressed as:
F = qE
Since the force acting on the charge is balanced, we have:
F = F' = q'E'
where q' represents the new magnitude of the mobile charge and E' is the new electric field at a distance of 2d from the negative plate.
Using the equation F = qE, we can rearrange it to:
q = F / E
Substituting the values, we have:
q = (q'E') / E
Since E is the same between the plates, we can simplify the equation to:
q = q' (E' / E)
Now, let's consider the relationship between E and E'. The magnitude of the electric field between the plates remains constant, meaning E = E'.
Therefore, we can conclude that q = q', which means the magnitude of the electric charge remains the same when the distance doubles between the negative plate and the mobile charge. It does not become 1/4 of the initial value.
So, the correct answer is that the magnitude of the electric charge remains the same.