AIIMS 2019 Physics Forces between charges MCQ Question

The ratio of the electrostatic force (Fₑ) to the magnetic force (Fₘ) between two protons moving parallel to each other can be derived from Coulomb's law and the Biot-Savart law. The electrostatic force is given by $Fₑ = \frac{k \cdot e^2}{r^2}$, where $k$ is Coulomb's constant and $e$ is the charge of the proton, while the magnetic force is $Fₘ = \frac{μ₀}{4π} \cdot \frac{e^2 v^2}{r^2}$ for two moving charges. The ratio $\frac{Fₑ}{Fₘ}$ simplifies to $\frac{v}{c}$, where $c$ is the speed of light, leading to a numerical value of approximately $4.5 \times 10^5$ when substituting $v = 4.5 \times 10^5 \, \text{m/s}$. Other options do not match this calculated ratio, making them incorrect.