SATHEE: Physics And Measurement Question 257

Physics And Measurement Question 257

Question: 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 $μ_{0}$ can be expressed in units of

Options:

A) $(\frac{h}{m e^{2}})$

B) $(\frac{h c}{m e^{2}})$

C) $(\frac{h}{c e^{2}})$

D) $(\frac{m c^{2}}{h e^{2}})$

Show Answer

Answer:

Correct Answer: C

Solution:

[c] Let $μ_{0}$ related with e, m, c and h as follows. $μ_{0} = k e^{a} m^{b} c^{c} h^{d}$

$[M L T^{- 2} A^{- 2}] = {[A T]}^{a} {[M]}^{b} {[L T^{- 1}]}^{c} {[M L^{2} T^{- 1}]}^{d}$

$- [M^{b + d} L^{c + 2 d} T^{a - c - d} A^{a}]$

On comparing both sides we get $a = - 2, b = 0, c = - 1, d = 1$

$∴ [μ_{0}] - [\frac{h}{c e^{2}}]$

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Physics And Measurement Question 257

Question: 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 μ0 can be expressed in units of

Options:

Answer:

Solution:

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Question: 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 $μ_{0}$ can be expressed in units of