A 2.00-nF parallel-plate capacitor is charged to an initial potential difference and then isolated. The dielectric material between the plates is mica, with a dielectric constant of 5.00. How much work is required to withdraw the mica sheet? [6]What is the potential difference of the capacitor after the mica is withdrawn? [4]
To determine the work required to withdraw the mica sheet, we need to consider the energy stored in the capacitor before and after the mica is removed.
The energy stored in a capacitor can be calculated using the formula:
U = 0.5 * C * V^2
Where U is the energy, C is the capacitance, and V is the potential difference across the capacitor.
In this case, the initial potential difference is not given, so let's denote it as V_initial.
Before removing the mica sheet, the energy stored in the capacitor can be calculated as:
U_initial = 0.5 * C * V_initial^2
To find the work required to withdraw the mica sheet, we need to determine the change in energy. Removing the mica will reduce the capacitance of the capacitor, effectively increasing the potential difference across the plates.
The final capacitance can be calculated by dividing the initial capacitance by the dielectric constant:
C_final = C / k
Where k is the dielectric constant.
The final potential difference of the capacitor can be calculated using the formula:
V_final = sqrt(2 * U_initial / C_final)
Now we have the final potential difference, we can calculate the energy stored in the capacitor after the mica is withdrawn:
U_final = 0.5 * C_final * V_final^2
The work required to withdraw the mica sheet can be calculated as the difference in energy:
Work = U_final - U_initial
Let's substitute the given values into the formulas to find the answers.
Using the given values:
C = 2.00 nF = 2.00 * 10^(-9) = 5.00
1. Calculate the initial energy:
U_initial = 0.5 * 2.00 * 10^(-9) * V_initial^2
2. Calculate the final capacitance:
C_final = (2.00 * 10^(-9)) / 5.00
3. Calculate the final potential difference:
V_final = sqrt(2 * U_initial / C_final)
4. Calculate the final energy:
U_final = 0.5 * C_final * V_final^2
5. Calculate the work required to withdraw the mica sheet:
Work = U_final - U_initial
The final potential difference across the capacitor can be calculated as V_final.