When charge is at rest then it creates only electric field not the magnetic field. A moving charge generates electric as well as magnetic field around it. If charge is moving with constant velocity then electric and magnetic field do not change with time, hence, it cannot produce electromagnetic wave. When charge is accelerated then time-varying electric and magnetic fields are created and thus electromagnetic wave is produced by accelerated charge. We know that the current-carrying wire creates magnetic field around it. If alternating current is flowing through the wire then it creates variable magnetic field around it and thus starts radiating electromagnetic waves. When a charged capacitor is connected across an inductor then charge starts oscillating between the plates of the capacitor. Normally one plate of the capacitor is connected to Earth and the other plate is connected to an antenna. Antenna radiates electromagnetic wave. Hertz successfully produced electromagnetic waves using such LC oscillator. Speed of electromagnetic wave in vacuum is constant and equal to `3 xx 10^8` m/s. But inside a medium the speed changes according to electrical and magnetic properties of the medium.
IF `mu_r and epsi_r ` are the relative permeability and relative premittivity of the medium then speed of light in that medium can be written as

Options

A. `(1)/(sqrt(mu_0 mu _r epsi_0 epis_(r)))`
B. `(1)/( sqrt((mu_0 epis_0))`
C. `(1)/(sqrt( mu_r epsi_r))`
D. `( sqrt(mu_r epsi_r))/( sqrt(mu_0 epsi_0))`

Explanation

To find the speed of light in a medium, we can derive it using the concepts of relative permeability and relative permittivity. Here’s a step-by-step solution:

### Step 1: Understanding the Speed of Light in Vacuum
The speed of light in vacuum (denoted as \( c \)) is a fundamental constant given by:
\[ c = 3 \times 10^8 \text{ m/s} \]

### Step 2: Speed of Light in a Medium
When light travels through a medium, its speed changes depending on the medium's electrical and magnetic properties. The speed of light in a medium (denoted as \( v \)) can be expressed in terms of the medium's permeability (\( \mu \)) and permittivity (\( \epsilon \)).

### Step 3: Formula for Speed of Light in a Medium
The speed of light in a medium is given by the formula:
\[ v = \frac{1}{\sqrt{\mu \epsilon}} \]
where \( \mu \) is the permeability of the medium and \( \epsilon \) is the permittivity of the medium.

### Step 4: Expressing Permeability and Permittivity
In terms of the relative permeability (\( \mu_r \)) and relative permittivity (\( \epsilon_r \)), we can express the permeability and permittivity of the medium as:
\[ \mu = \mu_0 \mu_r \]
\[ \epsilon = \epsilon_0 \epsilon_r \]
where \( \mu_0 \) and \( \epsilon_0 \) are the permeability and permittivity of free space (vacuum).

### Step 5: Substituting into the Speed Formula
Substituting the expressions for \( \mu \) and \( \epsilon \) into the speed formula gives:
\[ v = \frac{1}{\sqrt{\mu_0 \mu_r \epsilon_0 \epsilon_r}} \]

### Step 6: Simplifying the Expression
This can be rewritten as:
\[ v = \frac{1}{\sqrt{\mu_0 \epsilon_0}} \cdot \frac{1}{\sqrt{\mu_r \epsilon_r}} \]
Since \( \frac{1}{\sqrt{\mu_0 \epsilon_0}} = c \), we have:
\[ v = \frac{c}{\sqrt{\mu_r \epsilon_r}} \]

### Final Result
Thus, the speed of light in a medium can be expressed as:
\[ v = \frac{c}{\sqrt{\mu_r \epsilon_r}} \]