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 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%.