The effective length of a magnet is 31.4 cm and its pole strength is 0.5 Am. The magnetic moment, if it is bent in the form of a semicircle will be

Options

A. `0.1 Am^(2)`
B. `0.01 Am^(2)`
C. `0.2 Am^(2)`
D. `1.2 Am^(2)`

Explanation

To find the magnetic moment of a magnet when it is bent into the form of a semicircle, we can follow these steps:

### Step 1: Understand the given values
- Effective length of the magnet (L) = 31.4 cm
- Pole strength (m) = 0.5 Am

### Step 2: Convert the effective length into meters
Since we need to work in SI units, we convert the effective length from centimeters to meters:
\[ L = 31.4 \, \text{cm} = 31.4 \times 10^{-2} \, \text{m} = 0.314 \, \text{m} \]

### Step 3: Calculate the magnetic moment for a straight magnet
The magnetic moment (M) of a straight magnet is given by the formula:
\[ M = m \times L \]
Substituting the values:
\[ M = 0.5 \, \text{Am} \times 0.314 \, \text{m} = 0.157 \, \text{Am}^2 \]

### Step 4: Determine the effective length when bent into a semicircle
When the magnet is bent into a semicircle, the effective length becomes the diameter of the semicircle. The relationship between the effective length of the straight magnet and the semicircle is:
\[ L_{\text{semicircle}} = \frac{2L}{\pi} \]
Substituting the value of L:
\[ L_{\text{semicircle}} = \frac{2 \times 0.314 \, \text{m}}{\pi} \approx \frac{0.628}{3.14} \approx 0.2 \, \text{m} \]

### Step 5: Calculate the magnetic moment for the semicircular magnet
Now, we can calculate the magnetic moment for the semicircular magnet using the new effective length:
\[ M_{\text{semicircle}} = m \times L_{\text{semicircle}} \]
Substituting the values:
\[ M_{\text{semicircle}} = 0.5 \, \text{Am} \times 0.2 \, \text{m} = 0.1 \, \text{Am}^2 \]

### Final Answer
The magnetic moment when the magnet is bent into the form of a semicircle is:
\[ M_{\text{semicircle}} = 0.1 \, \text{Am}^2 \]

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