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 \(\mu_0\) can be expressed in units of :
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 :
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Write mu0 = h^a m^b c^d e^f and match dimensions, or use the dimensionless fine-structure constant.
Updated On: Nov 11, 2026
- \(\left(\frac{hc}{me^2}\right)\)
- \(\left(\frac{h}{me^2}\right)\)
- \(\left(\frac{h}{ce^2}\right)\)
- \(\left(\frac{mc^2}{he^2}\right)\)
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The Correct Option is C
Solution and Explanation
Step 1: Let \(\mu_0=k\,h^a m^b c^d e^f\). \([\mu_0]=MLT^{-2}A^{-2}\); \([h]=ML^2T^{-1}\), \([m]=M\), \([c]=LT^{-1}\), \([e]=AT\).
Step 2: A: \(f=-2\). M: \(a+b=1\). L: \(2a+d=1\). T: \(-a-d+f=-2\Rightarrow a=-d\).
Step 3: \(2a-a=1\Rightarrow a=1,\ d=-1,\ b=0\).
Step 4: \(\mu_0\propto\frac{h}{ce^2}\).
Answer: (3) \(\frac{h}{ce^2}\)
Step 2: A: \(f=-2\). M: \(a+b=1\). L: \(2a+d=1\). T: \(-a-d+f=-2\Rightarrow a=-d\).
Step 3: \(2a-a=1\Rightarrow a=1,\ d=-1,\ b=0\).
Step 4: \(\mu_0\propto\frac{h}{ce^2}\).
Answer: (3) \(\frac{h}{ce^2}\)
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