A long, straight wire carries a current \(I\) that increases linearly with time \(t\) according to \(I(t) = C t\), where \(C\) is a positive constant. Point \(P_1\) is located at a perpendicular distance \(r_0\) from the wire, where the magnetic field magnitude at time \(t = t_0\) is measured to be \(B_0\). Point \(P_2\) is located at a perpendicular distance \(2 r_0\) from the wire. What is the magnitude of the magnetic field at point \(P_2\) at time \(t = 3 t_0\) in terms of \(B_0\)?