A closed surface S is set up around a conducting wire that is connected to a battery and a switch, as shown in the figure. When the switch is closed, the free electrons within the wire begin to travel along it. During any given time interval, the number of electrons entering the closed surface S equals the number leaving it. Upon closing the switch, the electric field flux through the closed surface

Step-by-step solution

According to Gauss's law, the electric flux through a closed surface is given by = q_ enclosed ₀ . Initially, when the switch is open, the wire is electrically neutral, so the net charge enclosed by the surface S is zero ( q_ enclosed = 0 ). Thus, the initial electric flux is zero. When the switch is closed, current starts flowing. The problem explicitly states that the number of electrons entering the closed surface S equals the number leaving it during any given time interval. This means there is no net accumulat