The effective length of magnet is 31.4cm and its pole strength is 0.8Am. The magnetic moment, if it is bent in the form of a semicircle is…`A-m^(2)`.

Options

A. 1.2
B. 1.6
C. 0.16
D. 0.12

Explanation

To find the magnetic moment of a magnet bent in the form of a semicircle, we can follow these steps:

### Step 1: Understand the Given Information
- Effective length of the magnet (L) = 31.4 cm
- Pole strength (m) = 0.8 Am

### Step 2: Convert Length to Meters
Since the SI unit of length is meters, we need to convert the effective length from centimeters to meters:
\[ L = 31.4 \text{ cm} = \frac{31.4}{100} \text{ m} = 0.314 \text{ m} \]

### Step 3: Calculate the Radius of the Semicircle
When the magnet is bent into the shape of a semicircle, the effective length of the magnet becomes the circumference of the semicircle. The formula for the circumference (C) of a semicircle is:
\[ C = \pi r \]
Where \( r \) is the radius. Setting the circumference equal to the effective length:
\[ \pi r = 0.314 \text{ m} \]
Using \( \pi \approx 3.14 \):
\[ r = \frac{0.314}{\pi} = \frac{0.314}{3.14} \approx 0.1 \text{ m} \]

### Step 4: Calculate the Diameter
The diameter (d) of the semicircle, which is the distance between the two poles, is given by:
\[ d = 2r = 2 \times 0.1 \text{ m} = 0.2 \text{ m} \]

### Step 5: Calculate the Magnetic Moment
The magnetic moment (M) of a magnet is given by the formula:
\[ M = m \times L \]
Where \( m \) is the pole strength and \( L \) is the effective length. Substituting the values:
\[ M = 0.8 \text{ Am} \times 0.314 \text{ m} \]
Calculating this:
\[ M = 0.2512 \text{ A-m}^2 \]

### Final Answer
The magnetic moment when the magnet is bent in the form of a semicircle is approximately:
\[ M \approx 0.2512 \text{ A-m}^2 \]