Question:

A bar magnet has total length \( 2l = 20 \) units and the field point \( P \) is at a distance \( d = 10 \) units from the centre of the magnet. If the relative uncertainty of length measurement is 1%, then the uncertainty of the magnetic field at point P is:
bar magnet has total length 2l = 20 units

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When dealing with errors and uncertainties, remember to apply error propagation rules and consider the powers involved in the formulas.
Updated On: Mar 17, 2025
  • 10%
  • 4%
  • 5%
  • 3%
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The Correct Option is C

Solution and Explanation

The magnetic field at point \( P \) is proportional to \( \frac{1}{d^3} \). Given the uncertainty in length measurement, the uncertainty in the magnetic field can be calculated using the propagation of errors. Since the relative uncertainty in length is 1%, the relative uncertainty in the magnetic field will be three times that: \[ \text{Uncertainty in } B = 3%\times \text{Uncertainty in Length} \] Thus, the uncertainty in the magnetic field is 5%.
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