A charge q moving at uniform speed enters a cylindrical region in free space at t = 0 and leaves at $t=\tau$, as shown. Which graph represents total electric flux $\Phi(t)$ through the entire closed cylindrical surface?
Gauss’s law states that flux through any closed surface is enclosed charge divided by $\epsilon_0$. While the charge lies inside the cylinder, the flux is $q/\epsilon_0$, independent of its position. Before entry and after exit the enclosed charge is zero and so is the flux. The rectangular pulse from 0 to τ is graph D; its edge values at the instant of crossing do not affect this choice.
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