Two protons move parallel to each other, keeping distance $$r$$ between them, both moving with same velocity $$v$$. Then the ratio of the electric and magnetic force of interaction between them is

Two protons moving parallel to each other produce both electric and magnetic forces.

The electric force between the two protons is

$$F_E=\frac{1}{4\pi\epsilon_0}\frac{e^2}{r^2}$$

The magnetic force between two parallel moving charges is

$$F_B=\frac{\mu_0}{4\pi}\frac{e^2v^2}{r^2}$$

Therefore,  $$\frac{F_E}{F_B}=\frac{\frac{1}{4\pi\epsilon_0}\frac{e^2}{r^2}}{\frac{\mu_0}{4\pi}\frac{e^2v^2}{r^2}}$$

Using $$\mu_0\epsilon_0=\frac{1}{c^2}$$,

$$\frac{F_E}{F_B}=\frac{1}{\mu_0\epsilon_0v^2}=\frac{c^2}{v^2}$$

Therefore,  $${\frac{F_E}{F_B}=\frac{c^2}{v^2}}$$

Hence, the correct option is A.