6) A parallel plate capacitor is charged and then isolated. If the separation between the plates is increased, which one of the following statements is not correct?
A. Charge remains constant after it is isolated.
B. Potential difference across the plates decreases.
C. Potential difference across the plates increases.
D. Capacitance of the capacitor decreases.
Solution:
For an isolated capacitor, the charge \(Q\) remains constant after disconnecting from the source. The capacitance of a parallel plate capacitor is given by \[ C = \frac{\epsilon_0 A}{d}, \] so increasing the separation \(d\) decreases the capacitance. Since the voltage across the capacitor is given by \[ V = \frac{Q}{C}, \] a decrease in \(C\) results in an increase in \(V\). Therefore:
- Statement A is correct: Charge remains constant.
- Statement C is correct: Voltage increases.
- Statement D is correct: Capacitance decreases.
Hence, the incorrect statement is B, which claims that the potential difference decreases.
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