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Q.

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

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a

$μ_{0} ε_{0} \frac{E}{B}$

b

$μ_{0} ε_{0} {(\frac{B}{E})}^{2}$

c

$\frac{μ_{0}}{ε_{0}} \frac{E}{B}$

d

$\sqrt{μ_{0} ε_{0}} \frac{E}{B}$

answer is A.

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Detailed Solution

Speed of light , $c = \frac{1}{\sqrt{μ_{0} ε_{0}}}; Also, \frac{E}{B} = c$

therefore, $\sqrt{μ_{0} ε_{0}} \frac{E}{B}$ is dimensionless.

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