A beam of light travelling along $$X$$-axis is described by the electric field $$E_y = 900 \sin \omega\left(t - \dfrac{x}{c}\right)$$. The ratio of electric force to magnetic force on a charge $$q$$ moving along $$Y$$-axis with a speed of $$3 \times 10^7 \text{ m s}^{-1}$$ will be: [Given speed of light $$= 3 \times 10^8 \text{ m s}^{-1}$$]

We need to find the ratio of electric force to magnetic force on a charge moving along the Y-axis in an electromagnetic wave travelling along the X-axis.

The electric field is $$E_y = 900\sin\omega\left(t - \frac{x}{c}\right)$$ and for an EM wave travelling along the X-axis with $$E$$ along the Y-axis, the magnetic field $$B$$ is along the Z-axis given by $$B_z = \frac{E_y}{c}$$.

The charge $$q$$ moves along the Y-axis with speed $$v = 3 \times 10^7$$ m/s. Since the electric force is given by $$F_E = qE_y$$ and the magnetic force is $$F_B = qvB_z = qv\frac{E_y}{c}$$, we can form their ratio.

From the above expressions, we have $$\frac{F_E}{F_B} = \frac{qE_y}{qv \cdot E_y/c} = \frac{c}{v}$$. Substituting the values gives $$= \frac{3 \times 10^8}{3 \times 10^7} = 10$$.

Therefore, the correct answer is Option C: $$10:1$$.