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The magnetic dipole moment of a short magnetic dipole at a distant point along the equator of magnet has a magnitude of ‘X’ in SI units, tf the distance between the point and the magnet is halved then the magnitude of dipole moment win be
- a)2X
- b)(½)X
- c)x
- d)(⅛)X
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The magnetic dipole moment of a short magnetic dipole at a distant po...
The magnetic dipole moment is the product of either of pole strength and the magnetic length of dipole. Thus, it is independent of the distance of point at which it is measured. So. it remains unchanged, if the distance between point and the magnet is halved.
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The magnetic dipole moment of a short magnetic dipole at a distant po...
Explanation:
Magnetic Dipole Moment:
- The magnetic dipole moment is a measure of the strength of a magnetic dipole and is defined as the product of the magnitude of the magnetic pole and the distance between them.
- It is denoted by ‘m’ and its unit is ampere-meter square (A-m²) in SI units.
Effect of Distance on Magnetic Dipole Moment:
- As per the inverse square law, the magnetic field intensity due to a magnetic dipole reduces by the square of the distance from the dipole.
- Hence, if the distance between the point and the magnet is halved, the magnetic field intensity at that point becomes four times stronger.
- As the magnetic dipole moment is directly proportional to the magnetic field intensity, its magnitude also increases four times.
Mathematical Calculation:
- Let the magnetic dipole moment of the magnet at a distant point along the equator be X.
- When the distance between the point and the magnet is halved, the magnetic field intensity becomes four times stronger.
- Hence, the magnetic dipole moment at the new point becomes 4X.
- But, the question asks for the magnitude of the dipole moment, i.e., the absolute value of the dipole moment.
- Hence, the magnitude of the dipole moment at the new point becomes |4X| = 4|X|.
- As per the option given, the correct answer is (⅛)X, which is the absolute value of 4X divided by 8, i.e., |4X|/8 = (⅛)X.
Conclusion:
- When the distance between a point and a magnet is halved, the magnetic dipole moment at the new point becomes four times stronger.
- But, as the question asks for the magnitude of the dipole moment, it becomes eight times smaller than the original magnitude.
- Hence, the correct answer is (⅛)X.
Magnetic Dipole Moment:
- The magnetic dipole moment is a measure of the strength of a magnetic dipole and is defined as the product of the magnitude of the magnetic pole and the distance between them.
- It is denoted by ‘m’ and its unit is ampere-meter square (A-m²) in SI units.
Effect of Distance on Magnetic Dipole Moment:
- As per the inverse square law, the magnetic field intensity due to a magnetic dipole reduces by the square of the distance from the dipole.
- Hence, if the distance between the point and the magnet is halved, the magnetic field intensity at that point becomes four times stronger.
- As the magnetic dipole moment is directly proportional to the magnetic field intensity, its magnitude also increases four times.
Mathematical Calculation:
- Let the magnetic dipole moment of the magnet at a distant point along the equator be X.
- When the distance between the point and the magnet is halved, the magnetic field intensity becomes four times stronger.
- Hence, the magnetic dipole moment at the new point becomes 4X.
- But, the question asks for the magnitude of the dipole moment, i.e., the absolute value of the dipole moment.
- Hence, the magnitude of the dipole moment at the new point becomes |4X| = 4|X|.
- As per the option given, the correct answer is (⅛)X, which is the absolute value of 4X divided by 8, i.e., |4X|/8 = (⅛)X.
Conclusion:
- When the distance between a point and a magnet is halved, the magnetic dipole moment at the new point becomes four times stronger.
- But, as the question asks for the magnitude of the dipole moment, it becomes eight times smaller than the original magnitude.
- Hence, the correct answer is (⅛)X.
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The magnetic dipole moment of a short magnetic dipole at a distant point along the equator of magnet has a magnitude of ‘X’ in SI units, tf the distance between the point and the magnet is halved then the magnitude of dipole moment win bea)2Xb)(½)Xc)xd)(⅛)XCorrect answer is option 'C'. Can you explain this answer?
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