What are the dimensions of \( E/B \), where E and B are the electric and magnetic fields of an electromagnetic wave?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( [\mathrm{M^0\,L\,T^{-1}\,A^0}] \)
In an electromagnetic wave the field magnitudes are linked by the speed of light, \( E_0/B_0=c \). So \( E/B \) has the dimensions of a speed.
\( \begin{aligned} \left[\frac{E}{B}\right] &= [c] \\ &= [\mathrm{L\,T^{-1}}] \\ &= [\mathrm{M^0\,L\,T^{-1}\,A^0}] \end{aligned} \)
The units give the same result. With \( E \) in \( \mathrm{N\,C^{-1}} \) and \( B \) in \( \mathrm{N\,A^{-1}\,m^{-1}} \) (from \( F=qvB \) and \( F=IlB \)):
\( \begin{aligned} \frac{\mathrm{N\,C^{-1}}}{\mathrm{N\,A^{-1}\,m^{-1}}} &= \frac{\mathrm{A\,m}}{\mathrm{C}} \\ &= \frac{\mathrm{A\,m}}{\mathrm{A\,s}} \\ &= \mathrm{m\,s^{-1}} \end{aligned} \)
NCERT (2026-27):
Nature of Electromagnetic Waves – “… It is also seen from Maxwell’s equations that the magnitude of the electric and the magnetic fields in an electromagnetic wave are related as
\( B_0=(E_0/c) \)\( \qquad (8.10) \)”