In the circuit shown, an ideal battery of potential difference \(\varepsilon\) is connected to four resistors with resistances \(R_1 = R\), \(R_2 = 2R\), \(R_3 = 2R\), and \(R_4 = R\). Node \(P\) is located between \(R_1\) and \(R_2\), node \(Q\) is located between \(R_3\) and \(R_4\), and the bottom wire is connected to ground (\(0 \text{ V}\)). Switch \(S\) is initially closed and then opened. How does the electric potential at node \(P\) change when switch \(S\) is opened, and what physical reasoning accounts for this change?