The following figures show the arrangement of bar magnets in different configurations. Each magnet has a magnetic dipole moment . Which configuration has the highest net magnetic dipole moment?
Option 1
Option 2
Option 3
Option 4
Vector Nature: Magnetic dipole moment () is a vector quantity directed from the South pole to the North pole of the magnet .
Superposition Principle: The net magnetic dipole moment of a system of magnets is the vector sum of the individual dipole moments. For two magnets of equal magnetic moment inclined at an angle , the resultant moment is given by the parallelogram law of vector addition: Using the identity :
Maximization: The value of depends on . The cosine function decreases as the angle increases from to . Therefore, the resultant magnetic moment is highest when the angle between the magnetic moments is the smallest.
Conclusion: Without seeing the figures, standard physics principles dictate that the configuration with the most acute angle (closest to parallel alignment, ) will yield the maximum net dipole moment. Assuming Option 4 represents the configuration with the smallest angle (e.g., ), it is the correct choice.
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