QJEEM25Ph7f52: JEE Main 2025 Physics - Class 12 JEEM25Ph7f52 Solution: A bar magnet has total length units and the field point P is at …

Without considering uncentainity in $\ell$ .

$B=\frac{\mu_0}{4 \pi} \frac{m}{r^3}$

$\mathrm{B} \propto \frac{1}{\mathrm{r}^3}$

$\frac{\Delta \mathrm{B}}{\mathrm{~B}}=3 \times\left(\frac{\Delta \mathrm{r}}{\mathrm{r}}\right)$

$\%$ uncertainity in $\mathrm{B}=3 \%$

Method-2 :

With considering uncentainity in $\ell$ .

$\begin{aligned}& \mathrm{B} \propto \frac{1}{\mathrm{r}^3} \\& \frac{\Delta \mathrm{~B}}{\mathrm{~B}}=\frac{\Delta \ell}{\ell}+3 \times\left(\frac{\Delta \mathrm{r}}{\mathrm{r}}\right)=1+3 \times 1=4 \%\end{aligned}$

$\%$ uncertainity in $B=4 \%$