Physics


Dimensions of $$\displaystyle \frac{1}{\mu_{0}{\varepsilon_{0}}}$$ , where symbols have their usual meaning, are :


ANSWER

$$[\mathrm{L}^{2}\mathrm{T}^{-2}]$$


SOLUTION
Vaccum permittivity:
$${ F }_{ c }=\dfrac { 1 }{ 4\pi { \varepsilon   }_{ 0 } } \times \dfrac { { q }_{ 1 }{ q }_{ 2 } }{ { r }^{ 2 } } $$
Where $$\varepsilon_0  $$ is permttivity of vaccum.
Dimension will be $$[M^{-1}L^{-3}T^{4}I^{2}]$$

vaccum permeability:
$${ \mu  }_{ 0 }=4\pi \times { 10 }^{ -7 }\quad N/{ A }^{ 2 }$$
Dimensions will be $$[MLT^{-2}I^{-2}]$$

Dimensions for $$\dfrac { 1 }{ { \mu  }_{ 0 }{ \varepsilon  }_{ 0 } } $$ will be $$\dfrac { 1 }{ [{ M }^{ -1 }{ L }^{ -3 }{ T }^{ 4 }{ I }^{ 2 }]\times [{ M }^{ 1 }{ L }^{ 1 }{ T }^{ -2 }{ I }^{ -2 }] } =[L^2T^{-2}]$$
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Single Correct Medium Published on 18th 08, 2020
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