(A ): Speed of EM wave in a medium depends on electrical permittivity and magnetic permeability of the medium (R) E.M wave transport energy in the form of oscillating electric and magnetic fields

Options

A. Both 'A' and 'R' are true and 'R' is the correct explanation of 'A'.
B. Both 'A' and ’R' are true and 'R' is not the correct explanation of 'A
C. A' is true and 'R' is false
D. 'A' is false and R' is true

Answer

To solve the question regarding the properties of electromagnetic (EM) waves in a medium, we will analyze both statements provided:

### Step 1: Understanding the Speed of EM Waves in a Medium
The speed of electromagnetic waves in a medium is determined by the electrical permittivity (ε) and magnetic permeability (μ) of that medium. The formula for the speed of EM waves (v) in a medium can be expressed as:

\[ v = \frac{1}{\sqrt{\mu \cdot \epsilon}} \]

Where:
- \( \mu \) is the magnetic permeability of the medium.
- \( \epsilon \) is the electrical permittivity of the medium.

### Step 2: Identifying the Components of Permittivity and Permeability
In a medium, the electrical permittivity can be expressed as:

\[ \epsilon = \epsilon_0 \cdot \epsilon_r \]

And the magnetic permeability can be expressed as:

\[ \mu = \mu_0 \cdot \mu_r \]

Where:
- \( \epsilon_0 \) and \( \mu_0 \) are the permittivity and permeability of free space (vacuum).
- \( \epsilon_r \) and \( \mu_r \) are the relative permittivity and relative permeability of the medium.

### Step 3: Substituting into the Speed Formula
Substituting the expressions for permittivity and permeability into the speed formula gives:

\[ v = \frac{1}{\sqrt{\mu_0 \cdot \mu_r \cdot \epsilon_0 \cdot \epsilon_r}} \]

This shows that the speed of EM waves in a medium depends on both the electrical permittivity and magnetic permeability of the medium.

### Step 4: Analyzing the Energy Transport
Electromagnetic waves transport energy through oscillating electric and magnetic fields. This is a fundamental characteristic of EM waves, where the electric field (E) and magnetic field (B) oscillate perpendicular to each other and to the direction of wave propagation. This oscillation allows EM waves to carry energy through space.

### Step 5: Conclusion
Based on the analysis:
- Statement (A) is correct: The speed of EM waves in a medium does depend on the electrical permittivity and magnetic permeability of that medium.
- Statement (R) is also correct: EM waves do transport energy in the form of oscillating electric and magnetic fields.

Thus, both statements are true.

### Final Answer
Both statements (A) and (R) are correct.

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