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

• Correct answer
  A

  $4 \%$
• B

  $15 \%$
• C

  $5 \%$
• D

  $10 \%$

Solution

Magnetic field at $P, B=\frac{\mu_0}{4 \pi} \frac{m(2 l)}{r^3}$, where $m$ is the pole strength $\begin{aligned} \Rightarrow\left(\frac{\Delta B}{B} \times 100\right) & =\left(\frac{\Delta l}{l}\right) \times 100+3\left|\frac{\Delta r}{r}\right| \times 100 \\ & =1 \%+3 \%=4 \% \end{aligned}$

Hence, the correct answer is option: 'A'.