The ratio of contributions made by the eletric field and magnetic field components to the intensity of an `EM` wave is.

Options

A. `c : 1`
B. `c^(2) :1`
C. `1 : 1`
D. `sqrt(c) : 1`

Answer

To find the ratio of contributions made by the electric field and magnetic field components to the intensity of an electromagnetic (EM) wave, we can follow these steps:

### Step 1: Understand the Definition of Intensity
Intensity (I) of an electromagnetic wave is defined as the power (P) per unit area (A). Mathematically, it can be expressed as:
\[ I = \frac{P}{A} \]

### Step 2: Relate Intensity to Energy Density
The intensity of an EM wave can also be related to the energy density of the electric field (u_E) and the magnetic field (u_B). The energy density for the electric field is given by:
\[ u_E = \frac{1}{2} \epsilon_0 E^2 \]
And for the magnetic field, it is given by:
\[ u_B = \frac{1}{2} \frac{B^2}{\mu_0} \]

### Step 3: Express Intensity in Terms of Energy Density
The intensity can be expressed in terms of the energy densities:
\[ I_E = c \cdot u_E = c \cdot \frac{1}{2} \epsilon_0 E^2 \]
\[ I_B = c \cdot u_B = c \cdot \frac{1}{2} \frac{B^2}{\mu_0} \]
Where \( c \) is the speed of light in vacuum.

### Step 4: Find the Ratio of Electric Field Intensity to Magnetic Field Intensity
To find the ratio of the contributions of the electric field to the magnetic field, we can take the ratio of \( I_E \) to \( I_B \):
\[ \frac{I_E}{I_B} = \frac{c \cdot \frac{1}{2} \epsilon_0 E^2}{c \cdot \frac{1}{2} \frac{B^2}{\mu_0}} \]
The \( c \) and \( \frac{1}{2} \) terms cancel out:
\[ \frac{I_E}{I_B} = \frac{\epsilon_0 E^2}{\frac{B^2}{\mu_0}} \]

### Step 5: Use the Relationship Between E and B
In an electromagnetic wave, the electric field (E) and magnetic field (B) are related by the equation:
\[ E = cB \]
Where \( c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} \). Thus, we can substitute \( E = cB \) into the ratio:
\[ \frac{I_E}{I_B} = \frac{\epsilon_0 (cB)^2}{\frac{B^2}{\mu_0}} \]

### Step 6: Simplify the Expression
Substituting \( E = cB \):
\[ \frac{I_E}{I_B} = \frac{\epsilon_0 c^2 B^2}{\frac{B^2}{\mu_0}} \]
The \( B^2 \) terms cancel out:
\[ \frac{I_E}{I_B} = \epsilon_0 c^2 \cdot \mu_0 \]

### Step 7: Use the Relationship \( \epsilon_0 c^2 = \frac{1}{\mu_0} \)
Since \( \epsilon_0 c^2 = \frac{1}{\mu_0} \):
\[ \frac{I_E}{I_B} = 1 \]

### Conclusion
Thus, the ratio of contributions made by the electric field component to the magnetic field component to the intensity of an electromagnetic wave is:
\[ \frac{I_E}{I_B} = 1:1 \]