If two protons are moving with speed v=4.5 × 10^{5} ,m / s parallel to each other then ratio of ele

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4.Moving Charges and Magnetism

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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

A

$4.4 \times 10^{5}$

B

$2.2 \times 10^{5}$

C

$3.3 \times 10^{5}$

D

$1.1 \times 10^{5}$

(AIIMS-2019)

Solution

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 $(III).$

$\frac{F_{ E }}{F_{ M }}=\frac{9 \times 10^9 \times 4 \pi}{\left(4.5 \times 10^{5} m / s \right)^{2} 4 \pi \times 10^{-7}}$

$=4.4 \times 10^{5}$

Standard 12

Physics

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