Physics

# A physical quantity of the dimension of length that can be formed out of c, G and $\frac{e^{2}}{4\pi \epsilon _{0}}$ is [c is velocity of light, G is universal constant of gravitation and e is charge]

##### SOLUTION
Given,

$C,G,\dfrac{e^2}{4\pi \varepsilon_0}$

So,

$[L]=[C]^a,[G]^b[\dfrac{e^2}{4\pi \varepsilon_0}]^c$

$[L]=[LT^{-1}]^a,[ML^3T^{-2}]^b[ML^3T^{-2}]^c$

$[L]=L^{a+3b+3c}M^{-b+c}T^{-a-2b-2c}$

on comparing we get,

$a=3b+3c=1,$

$-b+c=0$

$a+2b+2c=0$

On solving we get,

$a=-2,b=\dfrac{1}{2},c=\dfrac{1}{2}$

Thus,

$L=\dfrac{1}{C^2}\sqrt{[\dfrac{Ge^2}{4\pi\varepsilon_0}]}$

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Subjective Medium Published on 18th 08, 2020
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