Dimensions of magnetic field intensity is

Options

A. `[M^(0)L^(0)T^(-1)A^(1)]`
B. `[MLT^(-1)A^(-1)]`
C. `[ML^(0)T^(-2)A^(-1)]`
D. `[MLT^(-2)A]`

Answer

To find the dimensions of magnetic field intensity (B), we can start from the formula that relates force (F), current (I), length (L), and magnetic field intensity (B). The relevant equation is:

\[ F = I \cdot L \cdot B \cdot \sin(\theta) \]

### Step-by-Step Solution:

1. **Identify the formula**:
We start with the equation \( F = I \cdot L \cdot B \cdot \sin(\theta) \).

2. **Rearrange the formula**:
To find the magnetic field intensity (B), we can rearrange the formula:
\[ B = \frac{F}{I \cdot L \cdot \sin(\theta)} \]

3. **Consider the dimensions of each variable**:
- The dimension of force (F) is given by:
\[ [F] = MLT^{-2} \]
- The dimension of current (I) is:
\[ [I] = A \]
- The dimension of length (L) is:
\[ [L] = L \]
- The angle (θ) is a trigonometric ratio and has no dimensions.

4. **Substituting the dimensions**:
Now, substituting the dimensions into the rearranged formula:
\[ [B] = \frac{[F]}{[I] \cdot [L]} = \frac{MLT^{-2}}{A \cdot L} \]

5. **Simplifying the expression**:
We can simplify the expression:
\[ [B] = \frac{MLT^{-2}}{AL} = \frac{M}{A} \cdot T^{-2} \]
This can be written as:
\[ [B] = ML^{0}T^{-2}A^{-1} \]

6. **Final result**:
Therefore, the dimensions of magnetic field intensity (B) are:
\[ [B] = ML^{0}T^{-2}A^{-1} \]

### Conclusion:
The correct dimensions of magnetic field intensity (B) are \( ML^{0}T^{-2}A^{-1} \).