Two magnets of a magnet is `16 cm`. Its pole strength is `250` milli.amp.m`. When it is cut into four equal pieces parallel to its axis, The magnetic length, pole strength and moments of each piece are: (respectively)

Options

A. `4cm,62.5milli Am,250 milli amp. Cm^(2)`
B. `8 cm,500 milli Am,400 milli amp. Cm^(2)`
C. `16 cm,250 milli Am,4000milli amp.cm^(2)`
D. `16 cm, 62.5 milli Am,0.01 A.m^(2)`

Explanation

To solve the problem step by step, we need to determine the magnetic length, pole strength, and magnetic moment of each piece after cutting the original magnet into four equal parts.

### Step 1: Determine the original parameters of the magnet
- The original length of the magnet (L) = 16 cm
- The original pole strength (m) = 250 milliampere-meter (mA·m)

### Step 2: Calculate the new pole strength after cutting
When the magnet is cut into four equal pieces parallel to its axis, the pole strength of each piece will be reduced to one-fourth of the original pole strength.

\[ \text{New pole strength} (m') = \frac{m}{4} = \frac{250 \, \text{mA·m}}{4} = 62.5 \, \text{mA·m} \]

### Step 3: Determine the magnetic length of each piece
Since the magnet is cut parallel to its axis, the magnetic length of each piece remains the same as the original length.

\[ \text{Magnetic length of each piece} = 16 \, \text{cm} = 0.16 \, \text{m} \]

### Step 4: Calculate the magnetic moment of each piece
The magnetic moment (M) of a magnet is given by the product of its pole strength and its magnetic length.

\[ \text{Magnetic moment} (M') = m' \times L = 62.5 \, \text{mA·m} \times 0.16 \, \text{m} = 10 \, \text{mA·m}^2 \]

### Summary of Results
- Magnetic length of each piece = 16 cm
- Pole strength of each piece = 62.5 mA·m
- Magnetic moment of each piece = 10 mA·m²

### Final Answer
The magnetic length, pole strength, and magnetic moment of each piece are:
- Magnetic Length: 16 cm
- Pole Strength: 62.5 mA·m
- Magnetic Moment: 10 mA·m²

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