In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, [E] and [B] stand for dimensions of electric and magnetic fields respectively. While `[ in_(0)]` and `[mu_(0)]` stand for dimensions of the permittivity and permeability of free space respectively. [L] and [T] are dimensions of length and time respectively. All the quantities are given in SI units.
The relation between [E] adn [B] is :-

Options

A. `[E]=[B][L][T]`
B. `[E]=[B][L]^(-1)[T]`
C. `[E]=[B][L][T]^(-1)`
D. `[E]=[B]=[L]^(-1)[T]^(-1)`

Answer

To find the relation between the dimensions of the electric field \([E]\) and the magnetic field \([B]\), we start with the fundamental relationship in electromagnetic theory.

### Step-by-Step Solution:

1. **Understanding the Relationship**:
The electric field \(\mathbf{E}\) and the magnetic field \(\mathbf{B}\) are related through the speed of light \(c\). The relationship can be expressed as:
\[ \mathbf{E} = c \mathbf{B} \]
where \(c\) is the speed of light in a vacuum.

2. **Finding the Dimension of Speed of Light**:
The speed of light \(c\) has dimensions of length per time:
\[ [c] = \frac{[L]}{[T]} \]

3. **Expressing the Electric Field in Terms of Magnetic Field**:
Rearranging the equation \(\mathbf{E} = c \mathbf{B}\) gives:
\[ [E] = [B] \cdot [c] \]

4. **Substituting the Dimension of Speed of Light**:
Substituting the dimension of \(c\) into the equation:
\[ [E] = [B] \cdot \frac{[L]}{[T]} \]

5. **Final Relation**:
This can be rearranged to express the relation between the dimensions of electric and magnetic fields:
\[ [E] = [B] \cdot [L][T]^{-1} \]

### Conclusion:
Thus, the relation between the dimensions of electric field \([E]\) and magnetic field \([B]\) is:
\[ [E] = [B] \cdot [L][T]^{-1} \]