Physics

Find the dimensions of: (i) Power, (ii) Forces and (iii) Permittivity of vacuum $(\varepsilon_o)$

SOLUTION

(I).The formula of power is

Power $P=\dfrac{W}{t}$

Now, the dimension of power is

$P=\dfrac{M{{L}^{2}}{{T}^{-2}}}{T}$

$P=M{{L}^{2}}{{T}^{-3}}$

(II).The formula of force is

$F=ma$

The dimension of force is

$F=ML{{T}^{-2}}$

(III).The formula of permittivity is

$F=\dfrac{1}{4\pi {{\varepsilon }_{0}}}\dfrac{q}{{{d}^{2}}}$

${{\varepsilon }_{0}}=\dfrac{q}{F{{d}^{2}}}$

$4\pi$ is a unit less so on neglect

So, the dimension of permittivity is

${{\varepsilon }_{0}}=\dfrac{{{\left[ TA \right]}^{2}}}{\left[ ML{{T}^{-2}} \right]\left[ {{L}^{2}} \right]}$

${{\varepsilon }_{0}}={{M}^{-1}}{{L}^{-3}}{{T}^{4}}{{A}^{2}}$

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Subjective Medium Published on 18th 08, 2020
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