The magnetic moment has dimensions of

Options

A. `V`
B. `2V`
C. `4V`
D. `-2V`

Explanation

To find the dimensions of the magnetic moment, we can follow these steps:

### Step 1: Understand the formula for magnetic moment
The magnetic moment (M) is defined as the product of current (I) and area (A). Therefore, we can express it as:
\[ M = I \times A \]

### Step 2: Identify the dimensions of current
The dimension of electric current (I) is represented in terms of the base unit of ampere (A). In dimensional analysis, we denote the dimension of current as:
\[ [I] = A^1 \]

### Step 3: Identify the dimensions of area
The area (A) can be expressed in terms of length. Since area is measured in square units (e.g., square meters), we can express its dimension as:
\[ [A] = L^2 \]

### Step 4: Combine the dimensions
Now, we can combine the dimensions of current and area to find the dimensions of magnetic moment:
\[ [M] = [I] \times [A] = A^1 \times L^2 \]

### Step 5: Write the final dimensional formula
Thus, the dimensional formula for magnetic moment can be expressed as:
\[ [M] = A^1 L^2 \]

### Final Answer
The magnetic moment has dimensions of \( A^1 L^2 \).

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