Step 1: List Maxwell's four equations.
Maxwell's equations are the four fundamental laws governing electromagnetism: (i) Gauss's law for electricity: $ \oint \vec{E}\cdot d\vec{A} = Q/\varepsilon_0 $ (ii) Gauss's law for magnetism: $ \oint \vec{B}\cdot d\vec{A} = 0 $ (iii) Faraday's law: $ \oint \vec{E}\cdot d\vec{l} = -d\phi_B/dt $ (iv) Ampere-Maxwell law: $ \oint \vec{B}\cdot d\vec{l} = \mu_0 i_c + \mu_0\varepsilon_0\, d\phi_E/dt $
Step 2: Focus on Gauss's law for magnetism.
Option (2) states $ \oint \vec{B}\cdot d\vec{A} = Q/\varepsilon_0 $, but the correct form is $ \oint \vec{B}\cdot d\vec{A} = 0 $. The right-hand side must always be zero because magnetic monopoles do not exist. There is no isolated magnetic charge analogous to electric charge $ Q $.
Step 3: Verify the other three options are correct.
Option (1) is the Ampere-Maxwell law - correct. Option (3) is Faraday's law of electromagnetic induction - correct. Option (4) is Gauss's law for electricity - correct.
Step 4: Understand why magnetic flux through a closed surface is zero.
Every magnetic field line that enters a closed surface must also exit, because field lines form closed loops (no monopoles). So the net flux through any closed surface is always zero.
Step 5: Identify the incorrect equation.
The equation in option (2) assigns a non-zero right-hand side to the magnetic Gauss law, which is physically wrong. The correct equation has zero on the right.
Step 6: Final answer.
\[ \boxed{\oint \vec{B}\cdot d\vec{A} = \frac{Q}{\varepsilon_0}\ \text{is incorrect; it should be }\ \oint \vec{B}\cdot d\vec{A} = 0} \]