Physics

Multiple Correct Answers Type
Which of the following pairs have the same dimensions?


ANSWER

$$h/e$$ and magnetic flux

Electric flux and $$a/ \epsilon_0$$


SOLUTION
$$\left[ h \right] =\left[ Joute\times second \right] =\left[ { ML }^{ 2 }{ T }^{ -1 } \right] $$
[Magnetic flux] $$=$$ [Magnetic field $$\times$$ Area]
$$\Rightarrow \quad \left[ \phi  \right] =\left[ { MTA }^{ -1 } \right] \left[ { L }^{ 2 } \right] $$
$$\Rightarrow \quad \left[ \phi  \right] =\left[ { ML }^{ 2 }{ TA }^{ -1 } \right] $$
And
        $$\left[ \dfrac { h }{ e }  \right] =\left[ \dfrac { { ML }^{ 2 }{ T }^{ -1 } }{ AT }  \right] =\left[ { ML }^{ 2 }{ T }^{ -2 }{ A }^{ -1 } \right] $$
[Electric flux] $$=\left[ E \right] \left[ A \right] =\left[ \dfrac { E }{ q }  \right] \left[ A \right] $$
$$\Rightarrow $$  [Electric flux] $$=\left[ \dfrac { F }{ IT }  \right] \left[ A \right] =\dfrac { \left[ { ML }T^{ -2 } \right] \left[ { L }^{ 2 } \right]  }{ AT } $$
                             $$=\left[ { ML }^{ 3 }{ T }^{ -3 }{ A }^{ -1 } \right] $$
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Multiple Correct Medium Published on 18th 08, 2020
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