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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