Two long coaxial solenoids of radius 2 cm and 4 cm respectively, have same number of turns per unit length and carry initially no currents. Current starts flowing in same direction in both solenoid simultaneously, such that both currents increases linearly with time. Instantaneous current in inner solenoid is double the current in outer solenoid. As a result of increasing currents in solenoids, a charged particle initially at rest between solenoids starts moving along a circular path of radius r, Find $r^2\left(inc{m}^2\right)$