If two protons are moving with speed $v=4.5 \times 10^{5} \,m / s$ parallel to each other then the ratio of electrostatic and magnetic force between them
AIIMS 2019, Diffcult
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The expression for electric force is given by,
$F_{ E }=\frac{k e^{2}}{r^{2}}$ $...(I)$
The expression for magnetic force is given by,
$F_{ M }=\frac{e^{2} V^{2} \mu_{0}}{4 \pi r^{2}}$ $...(II)$
Divide equation $(I)$ and $(I).$
$\frac{F_{ E }}{F_{ M }}=\frac{\frac{k e^{2}}{r^{2}}}{\frac{e^{2} V^{2} \mu_{0}}{4 \pi r^{2}}}$
$=\frac{k 4 \pi}{V^{2} \mu_{0}}$ $...(III)$
Substitute $9 \times 10^9$ for $k, 4.5 \times 10^{5} m / s$ for $V$ and $4 \pi \times 10^{-7}$ for $\mu_\circ$ in equation $(III).$
$\frac{F_{ E }}{F_{ M }}=\frac{9 \times 10^9 \times 4 \pi}{\left(4.5 \times 10^{5} m / s \right)^{2} 4 \pi \times 10^{-7}}$
$=4.4 \times 10^{5}$
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