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:
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When dealing with errors and uncertainties, remember to apply error propagation rules and consider the powers involved in the formulas.
The magnetic field at point \( P \) is inversely proportional to the cube of the distance, \( B \propto \frac{1}{d^3} \). The propagation of errors is used to determine the uncertainty in the magnetic field, considering the uncertainty in the length measurement.
Given a 1% relative uncertainty in length, the relative uncertainty in the magnetic field is three times this value:
\[
\text{Relative Uncertainty in } B = 3 \times \text{Relative Uncertainty in Length}
\]
Consequently, the uncertainty in the magnetic field is 3%.
