JEE Mains · Physics · STD 11 - 1. units,dimensions and measurement
If electronic charge \(e\), electron mass \(m\), speed of light in vacuum \(c\) and Planck 's constant \(h\) are taken as fundamental quantities, the permeability of vacuum \(\mu _0\) can be expressed in units of
- A \(\left( {\frac{h}{{m{e^2}}}} \right)\)
- B \(\left( {\frac{{hc}}{{m{e^2}}}} \right)\)
- C \(\left( {\frac{h}{{c{e^2}}}} \right)\)
- D \(\left( {\frac{{m{c^2}}}{{h{e^2}}}} \right)\)
Answer & Solution
Correct Answer
(C) \(\left( {\frac{h}{{c{e^2}}}} \right)\)
Step-by-step Solution
Detailed explanation
Let \(\mu_{0}\) related with \(e, m, c\) and \(h\) as follows. \(\mu_{0}=k e^{a} m^{b} c^{c} h^{d}\) \({\left[M L T^{-2} A^{-2}\right]=[A T]^{a}[M]^{b}\left[L T^{-1}\right]^{c}\left[M L^{2} T^{-1}\right]^{d}}\) \(=\left[M^{b+d} L^{c+2 d} T^{a-c-d} A^{a}\right]\) On comparingboth…
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