Relation between amplitudes of electric and Magnetic field is (A) \(E_{0}=B_{0}\) (B) \(E_{0}=\mathrm{cB}_{0}\) (C) \(E_{0}=\left(B_{0} / c\right)\) (D) \(E_{0}=\left(\mathrm{c} / \mathrm{B}_{0}\right)\)

In an electromagnetic wave, the electric field (E) and the magnetic field (B) are perpendicular to each other and vary sinusoidally in both space and time. The relationship between the magnitudes of electric and magnetic fields in an electromagnetic wave is given by: \[E = cB\] where E is the magnitude of the electric field, B is the magnitude of the magnetic field, and c is the speed of light in a vacuum (\(3 \times 10^8\) m/s).

Now that we have the relationship between the magnitudes of electric and magnetic fields, let's compare it with the given options: (A) \(E_{0}=B_{0}\): This option implies that the amplitudes of the electric and magnetic fields are equal. However, it does not take into account the speed of light. (B) \(E_{0}=cB_{0}\): This option correctly states the relationship between the amplitudes of electric and magnetic fields, with the speed of light included. Based on our earlier equation, this option is correct. (C) \(E_{0}=(B_{0} / c)\): This option incorrectly implies that the amplitude of the electric field is equal to the amplitude of the magnetic field divided by the speed of light. (D) \(E_{0}=(c / B_{0})\): This option incorrectly implies that the amplitude of the electric field is equal to the speed of light divided by the amplitude of the magnetic field.

Based on our comparison, the correct relationship between the amplitudes of electric and magnetic fields in an electromagnetic wave is Option (B): \(E_{0} = cB_{0}\)