Consider a sort magnetic dipole of magnetic length 10cm. Find its geometric length.

Options

A. 12 cm
B. 5 cm
C. 3 cm
D. 4 cm

Answer

To solve the problem of finding the geometric length of a short magnetic dipole given its magnetic length, we can follow these steps:

### Step 1: Understand the Definitions
- **Magnetic Length (ML)**: This is the distance between the north and south poles of the magnet. In this case, it is given as 10 cm.
- **Geometric Length (GL)**: This is the total length of the magnet from one end to the other.

### Step 2: Use the Relationship Between Magnetic Length and Geometric Length
There is a known relationship between the magnetic length and the geometric length of a magnet:
\[ \text{Magnetic Length (ML)} = \frac{5}{6} \times \text{Geometric Length (GL)} \]

### Step 3: Rearrange the Formula to Find Geometric Length
To find the geometric length, we can rearrange the formula:
\[ \text{Geometric Length (GL)} = \frac{6}{5} \times \text{Magnetic Length (ML)} \]

### Step 4: Substitute the Given Magnetic Length
Now we substitute the given magnetic length (ML = 10 cm) into the rearranged formula:
\[ \text{Geometric Length (GL)} = \frac{6}{5} \times 10 \, \text{cm} \]

### Step 5: Calculate the Geometric Length
Now, perform the calculation:
\[ \text{Geometric Length (GL)} = \frac{6 \times 10}{5} = \frac{60}{5} = 12 \, \text{cm} \]

### Final Answer
Thus, the geometric length of the magnetic dipole is **12 cm**.

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