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4.Moving Charges and Magnetism
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Two protons move parallel to each other, keeping distance $r$ between them, both moving with same velocity $\vec V\,$. Then the ratio of the electric and magnetic force of interaction between them is
A
$c^2 / v^2$
B
$2c^2 / v^2$
C
$c^2 / 2v^2$
D
None
Solution
Electric force $\mathrm{Fe}=\mathrm{kq}_{1} \mathrm{q}_{2} / \mathrm{r}^{2}=\mathrm{kq}^{2} / \mathrm{r}^{2}$
Magnetic force $=\mathrm{qv}\left(\frac{\mu_{0}}{4 \pi} \times \frac{\mathrm{qv}}{r^{2}}\right)$
$\mathrm{F}_{\mathrm{m}}=\mathrm{q}^{2} \mathrm{v}^{2}\left(\frac{\mu_{0}}{4 \pi}\right) \frac{1}{\mathrm{r}^{2}}$
$\frac{F e}{F_{m}}=\frac{k}{v^{2}\left(\frac{\mu_{0}}{4 \pi}\right)}=\frac{1}{v^{2} \varepsilon_{0} \mu_{0}}=\frac{c^{2}}{v^{2}}$
Standard 12
Physics
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