Recall the basic properties of a plane electromagnetic wave

For a plane electromagnetic wave in free space:

• The electric field $\vec E$ and magnetic field $\vec B$ are mutually perpendicular.
• Both are perpendicular to the direction of propagation.
• The direction of propagation is along $\vec E \times \vec B$.
• Their magnitudes satisfy $E_0 = cB_0$ so $\frac{E_0}{B_0}=c \quad \text{and} \quad \frac{B_0}{E_0}=\frac{1}{c}.$

Check statement (A)

Statement (A): In a plane electromagnetic wave electric field and magnetic field must be perpendicular to each other and direction of propagation of wave should be along electric field or magnetic field.

• First part is true: $\vec E \perp \vec B$.
• Second part is false: the wave propagates perpendicular to both $\vec E$ and $\vec B$, not along either one.

Hence, (A) is false.

Check statement (B)

Statement (B): The energy in electromagnetic wave is divided equally between electric and magnetic fields.

Energy density due to electric field: $u_E = \frac{1}{2}\varepsilon_0 E^2$

Energy density due to magnetic field: $u_B = \frac{B^2}{2\mu_0}$

Using $E=cB$ and $c^2=\frac{1}{\mu_0\varepsilon_0}$, $u_B = \frac{B^2}{2\mu_0} = \frac{1}{2}\varepsilon_0 E^2 = u_E$

Therefore, (B) is true.

Check statement (C)

Statement (C): Both electric field and magnetic field are parallel to each other and perpendicular to the direction of propagation of wave.

This is incorrect because in an electromagnetic wave, $\vec E \perp \vec B$ not parallel.

Hence, (C) is false.

Check statement (D)

Statement (D): The electric field, magnetic field and direction of propagation of wave must be perpendicular to each other.

This is exactly the correct description of a plane electromagnetic wave.

Hence, (D) is true.

Check statement (E)

Statement (E): The ratio of amplitude of magnetic field to the amplitude of electric field is equal to speed of light.

But actually, $E_0 = cB_0$ so $\frac{B_0}{E_0}=\frac{1}{c}$ not $c$.

Hence, (E) is false.

Identify the correct statements

True statements are: $\boxed{(B) \text{ and } (D)}$

Match with options

• A: (D) only → incorrect
• B: (B) and (D) only → correct
• C: (B), (C) and (E) only → incorrect
• D: (A), (B) and (E) only → incorrect

Therefore, the correct option is $\boxed{\text{B}}$