A hypothetical bar magnet AB is cut into two equal parts. One part is ...
The magnetic moment of the combination so formed will be zero because the pole strength gets neutralised. This neutralisation of the pole strength occurs because the magnet is cut into 2 equal parts and hence net magnetic moment is zero.
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A hypothetical bar magnet AB is cut into two equal parts. One part is ...
Introduction:
When a bar magnet is cut into two equal parts, each part will still possess its own magnetic field. The magnetic moment of a magnet depends on its strength and orientation. In this scenario, we will analyze the magnetic moments of the two combinations formed by placing one part of the magnet over the other.
Magnetic Moment of a Bar Magnet:
The magnetic moment of a magnet is defined as the product of its pole strength and the distance between its poles. Mathematically, it is given by the equation:
Magnetic Moment (M) = Pole Strength (m) × Distance between Poles (d)
Combination 1: North Pole to South Pole Alignment:
In this combination, the two cut pieces are aligned in such a way that the north pole of one piece is placed over the south pole of the other piece.
Magnetic Moment Calculation:
1. The pole strength of each individual piece remains the same as it was before cutting the magnet.
2. The distance between the poles of each individual piece also remains the same.
3. When the two pieces are combined, the net magnetic moment can be found by adding the magnetic moments of the individual pieces.
4. Since the pole strengths and distances are the same for each piece, the magnetic moments will add up to give twice the magnetic moment of a single piece.
- Net Magnetic Moment (Combination 1) = 2M
Combination 2: Like Poles Facing Each Other:
In this combination, the two cut pieces are aligned in such a way that the north pole of one piece is placed over the north pole of the other piece.
Magnetic Moment Calculation:
1. The pole strength of each individual piece remains the same as it was before cutting the magnet.
2. The distance between the poles of each individual piece also remains the same.
3. When the two pieces are combined, the net magnetic moment can be found by subtracting the magnetic moment of one piece from the magnetic moment of the other piece.
4. Since the pole strengths and distances are the same for each piece, the magnetic moments will cancel each other out.
- Net Magnetic Moment (Combination 2) = 0
Conclusion:
- When the two cut pieces of the bar magnet are aligned with north pole to south pole arrangement, the net magnetic moment of the combination is twice the magnetic moment of a single piece.
- When the two cut pieces of the bar magnet are aligned with like poles facing each other, the net magnetic moment of the combination is zero.