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1.Units, Dimensions and Measurement
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The dimensions of ${\left( {{\mu _0}{\varepsilon _0}} \right)^{ - \frac{1}{2}}}$ are
A$L^{1/2}T^{-1/2}$
B$L^{-1}T$
C$LT^{-1}$
D$L^{1/2}T^{1/2}$
(AIPMT-2011) (AIPMT-2012)
Solution
The, speed, of, the, light, in, vacuum, is
$c = \frac{1}{{\sqrt {{\mu _0}{\varepsilon _0}} }} = {\left( {{\mu _0}{\varepsilon _0}} \right)^{ – 1/2}}$
$\therefore \,\left[ {{{\left( {{\mu _0}{\varepsilon _0}} \right)}^{ – 1/2}}} \right] = \left[ c \right] = \left[ {L{T^{ – 1}}} \right]$
$c = \frac{1}{{\sqrt {{\mu _0}{\varepsilon _0}} }} = {\left( {{\mu _0}{\varepsilon _0}} \right)^{ – 1/2}}$
$\therefore \,\left[ {{{\left( {{\mu _0}{\varepsilon _0}} \right)}^{ – 1/2}}} \right] = \left[ c \right] = \left[ {L{T^{ – 1}}} \right]$
Standard 11
Physics
