Which of the following is /are correct ?

Options

A. Electric and magnetic fields, oscillating in space and time can sustain each
B. Electromagnetic waves can carry energy as well as momentum
C. Electromagnetic waves can event mechanical pressure
D. All of these

Answer

To determine which of the statements regarding electromagnetic waves is correct, we will analyze each statement step by step.

### Step 1: Analyze the first statement
**Statement 1:** Electric and magnetic fields oscillating in space and time can sustain each other.

- **Explanation:** In electromagnetic waves, the electric field (E) and magnetic field (B) oscillate perpendicular to each other and to the direction of wave propagation. For example, if the electric field oscillates in the y-direction and the magnetic field in the z-direction, the wave propagates in the x-direction. The oscillation of these fields is described by the equations:
- E = E₀ sin(ωt - kx)
- B = B₀ sin(ωt - kx)

This shows that the electric and magnetic fields sustain each other, confirming that this statement is true.

### Step 2: Analyze the second statement
**Statement 2:** Electromagnetic waves can carry energy as well as momentum.

- **Explanation:** Electromagnetic waves indeed carry energy, which can be expressed in terms of the electric and magnetic fields. The energy density (u) of an electromagnetic wave is given by:
- u = (1/2)ε₀E² + (1/2μ₀)B²
The momentum (p) of an electromagnetic wave can be related to its energy (U) by the equation:
- p = U/c
where c is the speed of light. Thus, electromagnetic waves carry both energy and momentum, making this statement true as well.

### Step 3: Analyze the third statement
**Statement 3:** Electromagnetic waves can cause mechanical pressure.

- **Explanation:** When electromagnetic waves strike a surface, they exert pressure. The mechanical pressure (P) exerted by an electromagnetic wave can be calculated as:
- P = u/c for perfectly absorbing surfaces
- P = 2u/c for perfectly reflecting surfaces
where u is the energy density of the wave. This indicates that electromagnetic waves can indeed cause mechanical pressure, confirming that this statement is also true.

### Conclusion
After analyzing all three statements, we find that all of them are correct. Therefore, the answer to the question is:

**Answer:** All of the above statements are correct (Option 4).

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