Force Between Two Moving Charges
Category : JEE Main & Advanced
If two charges \[{{q}_{1}}\] and \[{{q}_{2}}\] are moving with velocities v1 and v2 respectively and at any instant the distance between them is r, then .
Magnetic force between them is \[{{F}_{m}}=\frac{{{\mu }_{0}}}{4\pi }.\frac{{{q}_{1}}{{q}_{2}}\,{{v}_{1}}{{v}_{2}}}{{{r}^{2}}}\] .... (i)
and Electric force between them is \[{{F}_{e}}=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{{{q}_{1}}{{q}_{2}}}{{{r}^{2}}}\] .... (ii)
From equation (i) and (ii) \[\frac{{{F}_{m}}}{{{F}_{e}}}={{\mu }_{0}}{{\varepsilon }_{0}}{{v}^{2}}\] but \[{{\mu }_{0}}{{\varepsilon }_{0}}=\frac{1}{{{c}^{2}}}\];
where c is the velocity of light in vacuum. So \[\frac{{{F}_{m}}}{{{F}_{e}}}={{\left( \frac{v}{c} \right)}^{2}}\]
As \[v<c\] so \[{{F}_{m}}<{{F}_{e}}\]
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