Discussion

The dimensions of \(\frac{B}{E}\) are (B- Magnetic induction, E-electric field intensity)

A.\(M^{0}L^{-2}T^{1}\)
B.\(M^{0}L^{-1}T^{2}\)
C.\(M^{0}L^{1}T^{1}\)
D.\(M^{0}L^{-1}T^{1}\)
E.\(M^{0}L^{1}T^{-1}\)

Answer: D

The dimensions are \(M^{0}L^{-1}T^{1}\).

For an electromagnetic wave \(E = cB\), so \(\frac{B}{E} = \frac{1}{c}\), the reciprocal of a speed. Speed has dimensions \([LT^{-1}]\), so

\[ \left[\frac{B}{E}\right] = [L^{-1}T] \]

Equivalently, \(F = qE = qvB\) shows \(\frac{E}{B}\) is a velocity. \(M^{0}L^{1}T^{-1}\) is the dimension of \(\frac{E}{B}\), the inverted ratio.

Numerically, \(\frac{B}{E} = \frac{1}{c} \approx 3.3 \times 10^{-9}\) s m^-1 for a wave in vacuum, which carries the same dimensions.

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