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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Units and Dimensions

NTA Abhyas 2020 · Physics · Units and Dimensions

If E and B denote electric and magnetic fields respectively, which...

If EE and BB denote electric and magnetic fields respectively, which of the following is dimensionless?

Options

  1. Aμ0ε0EB\sqrt{{\mu}_{0}{ε}_{0}}\dfrac{E}{B}
  2. Bμ0ε0EB{\mu}_{0}{ε}_{0}\dfrac{E}{B}
  3. C{\mu}_{0}{ε}_{0}{\left(\dfrac{B}{E}\right)}^{2}
  4. Dμ0EBε0\dfrac{{μ}_{0}E}{B{ε}_{0}}

Correct answer

A. μ0ε0EB\sqrt{{\mu}_{0}{ε}_{0}}\dfrac{E}{B}

Step-by-step solution

EB=c\dfrac{E}{B} = c (Velocity of light if we consider free space)and1μ0ε0=cand \dfrac{1}{\sqrt{{\mu}_{0}{ε}_{0}}} = c

So μ0ε0EB\sqrt{{\mu}_{0}{ε}_{0}}\dfrac{E}{B} is dimensionless.
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