Basic Maths and Units and DimensionsEasy
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
A.
B.
C.
D.
Solution
μ0 = keambcchd
[MLT-2A-2] = [AT]a [M]b [LT-1]c [ML2T-1]d
= [Mb+dLc+2d Ta - c - d Aa]
Comparing a = - 2
b + d = 1
c + 2d = 1
a - c - d = - 2
Solving a = - 2, b = 0, c = - 1, d = 1
[μ0] =
Option (3)
[MLT-2A-2] = [AT]a [M]b [LT-1]c [ML2T-1]d
= [Mb+dLc+2d Ta - c - d Aa]
Comparing a = - 2
b + d = 1
c + 2d = 1
a - c - d = - 2
Solving a = - 2, b = 0, c = - 1, d = 1
[μ0] =
Option (3)
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