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The concept of potential difference is all about the voltage between two points, in this case, the two plates of a capacitor. Initially, when the plates are connected to a 6.00 V battery, the potential difference across them is simply 6.00 V.
But what happens when we disconnect the battery and change the spacing of the plates? The potential difference isn't fixed to 6 V anymore because it's not being held constant by the battery. Instead, it depends on the charge already present and the new plate spacing.

To find the final potential difference after altering the separation, use the formula:

• Initial charge on the plates: \( Q = C_i \times V \)
• Final potential difference: \( V_f = \frac{Q}{C_f} \)

Given that the initial capacitance and initial potential difference were known, and assuming the charge remains constant, the new potential difference was recalculated to be approximately 16.01 V once the plates were pulled further apart.

Stored energy in a capacitor is the energy kept within for future use. Initially, when connected to the battery, the energy is stored as electrostatic potential energy. It is determined by the initial capacitance and the initial voltage. Calculated using:

• Initial stored energy: \( U_i = \frac{1}{2} C_i V^2 \)

The initial energy was found to be \( 4.509 \times 10^{-11} \) J.
After changing the separation, the initial energy configuration changes because the capacitance changes while the charge stays the same.
To find the final stored energy:

• Final energy: \( U_f = \frac{1}{2} C_f V_f^2 \)

The new capacitance and altered voltage result in a final stored energy of \( 1.20 \times 10^{-10} \) J, reflecting the system's increased potential energy due to the increased separation.

Work done relates to the energy required to move changes within the capacitor. When the plates are pulled apart, energy is required to physically separate charged plates against the attractive electrostatic force.
The work done is calculated by measuring the difference in energy before and after the plates are separated. Simply put, you compare the initial energy and the final energy:

• Work done: \( W = U_f - U_i \)

In this exercise, after finding both the initial and final stored energies, the work calculated required to separate the plates was \( 7.49 \times 10^{-11} \) J.
This value gives insight into the energy balance and changes occurring when the field configuration is modified by varying plate distances. It's a crucial calculation showing how energy is conserved and transformed in such a system.