A 2.0 nF parallel plate capacitor with a sheet of mylar (k= 3.1) filling the space between the plates is charged to a potential difference of 90 V and is them disconnected. How much work would be required to completely remove the sheet of mylar from the space between the two plates?
To determine the work required to remove the sheet of mylar from the space between the plates, we need to consider the stored energy in the capacitor when it is charged and compare it to the situation when the mylar is removed.
The energy stored in a charged capacitor can be calculated using the formula:
E = (1/2) * C * V^2
Where E is the energy stored, C is the capacitance, and V is the potential difference.
In this case, the capacitance is given as 2.0 nF (nanofarads) and the potential difference is 90 V. We can calculate the initial energy stored in the capacitor as follows:
E_initial = (1/2) * (2.0 * 10^-9 F) * (90 V)^2
Next, we need to consider the situation when the mylar is removed. As the mylar is removed, the dielectric constant changes, resulting in a change in the capacitance. We assume that the mylar is completely removed, so the new capacitance would be that of the capacitor without any material between the plates. The formula for the new capacitance is:
C_new = (1 / (k * ε0)) * A / d
Where C_new is the new capacitance, k is the relative permittivity (dielectric constant) of the vacuum, ε0 is the permittivity of free space (8.85 x 10^-12 F/m), A is the area of the plates, and d is the distance between the plates.
Since we are considering a parallel plate capacitor, the area (A) and distance (d) between the plates are constant in this case. Therefore, we can simplify the formula to:
C_new = (1 / (k * ε0)) * C_original
Substituting the given values, we have:
C_new = (1 / (3.1 * 8.85 x 10^-12 F/m)) * 2.0 x 10^-9 F
Finally, we can calculate the final energy stored in the capacitor after the mylar is removed:
E_final = (1/2) * C_new * V^2
To find the work required to remove the mylar, we subtract the final energy from the initial energy:
Work = E_final - E_initial
By substituting the values and performing the calculations, we can determine the amount of work required to completely remove the sheet of mylar from the space between the two plates.