If E and B denote electric and magnetic fields respectively, which of following is dimensionless

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8.Electromagnetic waves

easy

If $E$ and $B$ denote electric and magnetic fields respectively, which of the following is dimensionless

A

$\sqrt {{\mu _0}{\varepsilon _0}} \frac{E}{B}$

B

$ {{\mu _0}{\varepsilon _0}} \frac{E}{B}$

C

${\mu _0}{\varepsilon _0}{\left( {\frac{B}{E}} \right)^2}$

D

$\frac{E}{{{\varepsilon _0}}}\frac{{{\mu _0}}}{B}$

Solution

Speed of light, $c=\frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}}$

Also, $\frac{E}{B}=c$

Therefore, $\sqrt{\mu_{0} \varepsilon_{0}} \frac{E}{B}$ is dimensionless.

Standard 12

Physics

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