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To develop this problem we will apply the concept of energy conservation. For which the work carried out must be equivalent to the potential energy stored on the capacitor. We will start by finding the capacitance to later be able to calculate the energy and therefore the work in the capacitor
Here,
C = Capacitance
V = Potential difference between the plates
Q = Charge between the capacitor plates
At the same time the energy stored in the capacitor can be defined as,
We will start by finding the value of the capacitance, so we will have to,
Finally using the expression for the energy we have that,
Therefore the minimum amount of work that must be done in charging this capacitor is