Two electric dipoles of dipole moments $$1.2 \times 10^{-30}$$ Cm and $$2.4 \times 10^{-30}$$ Cm are placed in two different uniform electric fields of strengths $$5 \times 10^4$$ N C$$^{-1}$$ and $$15 \times 10^4$$ N C$$^{-1}$$ respectively. The ratio of maximum torque experienced by the electric dipoles will be $$\frac{1}{x}$$. The value of $$x$$ is _____.

The torque experienced by an electric dipole in a uniform electric field is given by:

$$\tau = pE\sin\theta$$

The maximum torque occurs when $$\sin\theta = 1$$ (i.e., $$\theta = 90°$$):

$$\tau_{max} = pE$$

For dipole 1:

$$\tau_1 = p_1 E_1 = 1.2 \times 10^{-30} \times 5 \times 10^4 = 6.0 \times 10^{-26} \text{ N m}$$

For dipole 2:

$$\tau_2 = p_2 E_2 = 2.4 \times 10^{-30} \times 15 \times 10^4 = 36.0 \times 10^{-26} \text{ N m}$$

The ratio of maximum torques:

$$\frac{\tau_1}{\tau_2} = \frac{6.0 \times 10^{-26}}{36.0 \times 10^{-26}} = \frac{6}{36} = \frac{1}{6}$$

Since the ratio is given as $$\frac{1}{x}$$:

$$\frac{1}{x} = \frac{1}{6}$$ $$x = 6$$

Therefore, the value of $$x$$ is 6.