MCQ
The dimensions of ${\left( {{\mu _0}{\varepsilon _0}} \right)^{ - \frac{1}{2}}}$ are
- A$L^{1/2}T^{-1/2}$
- B$L^{-1}T$
- ✓$LT^{-1}$
- D$L^{1/2}T^{1/2}$
✓
Answer
Correct option: C.
$LT^{-1}$
c
The, speed, of, the, light, in, vacuum, is
$c = \frac{1}{{\sqrt {{\mu _0}{\varepsilon _0}} }} = {\left( {{\mu _0}{\varepsilon _0}} \right)^{ - 1/2}}$
$\therefore \,\left[ {{{\left( {{\mu _0}{\varepsilon _0}} \right)}^{ - 1/2}}} \right] = \left[ c \right] = \left[ {L{T^{ - 1}}} \right]$
The, speed, of, the, light, in, vacuum, is
$c = \frac{1}{{\sqrt {{\mu _0}{\varepsilon _0}} }} = {\left( {{\mu _0}{\varepsilon _0}} \right)^{ - 1/2}}$
$\therefore \,\left[ {{{\left( {{\mu _0}{\varepsilon _0}} \right)}^{ - 1/2}}} \right] = \left[ c \right] = \left[ {L{T^{ - 1}}} \right]$
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