Step 1: According to Gauss’s Law for magnetism: \[ \oint_S \mathbf{B} \cdot d\mathbf{A} = 0 \] where \( \mathbf{B} \) is the magnetic field and \( d\mathbf{A} \) is the infinitesimal area element over a closed surface.
Step 2: This law states that the net magnetic flux through a closed surface is always zero because magnetic monopoles do not exist; instead, magnetic field lines always form closed loops.
Step 3: Since every magnetic field line that enters a closed surface must exit, the total inward and outward flux cancel each other out, leading to a net flux of zero.
A closed-loop system has the characteristic equation given by: $ s^3 + k s^2 + (k+2) s + 3 = 0 $.
For the system to be stable, the value of $ k $ is: