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:

 

• A. 10\%
• B. 4\%
• C. 5\%
• D. 3\%

Hint:

When dealing with errors and uncertainties, remember to apply error propagation rules and consider the powers involved in the formulas.

Answer 1

The Correct Option is C

The magnetic field at point \( P \) is inversely proportional to the cube of the distance (\( \frac{1}{d^3} \)). Considering the uncertainty in length measurement, the propagation of errors is applied to determine the uncertainty in the magnetic field. A 1% relative uncertainty in length results in a three-fold relative uncertainty in the magnetic field: \[ {Uncertainty in } B = 3\% \times {Uncertainty in Length} \] Consequently, the uncertainty in the magnetic field is determined to be 5%.