Acceleration can be defined as the change of speed in an instant of time, that is
Here,
Final velocity
Initial velocity
Change in time
From this expression we will calculate the requested values replacing the variables in each of the given terms
PART A) The values under this condition are:
Replacing,
PART B ) The values under this condition are:
Replacing,
Therefore the acceleration in the second time interval is
PART C) The values under this condition are:
Replacing,
Answer:
a) In a parallel plate capacitor the capacitance is
So, in order to halve the capacitance the plate separation should be twice the original distance.
b) Same question as (a).
c) According to the above equations, the charge stored in a capacitor is directly proportional to the plate separation.
In order to halve the charge stored the plate separation should be half the original distance.
d) Same question as (c).
e) The energy stored in a capacitor is
In order to halve the energy stored in the capacitor, the plate separation should be twice the original distance.
f) Same question as (e).
g) The energy density is given by the following equation
As it turns out, the energy density is independent from the geometric factors. This makes sense, because the electric field in a parallel field capacitor is independent from the distance.