Question

The magnetic needle has magnetic moment $ 8.7\times 10^{-2}\,A \,m^{2} $ and moment of inertia $ 11.5\times 10^{-6}\,kg \,m^{2} $ . It performs 10 complete oscillations in $ 6.70\,s, $ what is the magnitude of the magnetic field?

• A. $ 0.012\,T $
• B. $ 0.120\,T $
• C. $ 1.200\,\,T $
• D. $ 2.10\,\,T $

Answer 1

Answer: (A)

$m=8.7 \times 10^{-2} A-m^{2}$
$l=11.5 \times 10^{-6} k h-m^{2}$
$T=0.67 s$
$\Rightarrow $ From the formula $T=2 \pi \sqrt{\frac{l}{m B}}$
$ \Rightarrow B=\frac{4 \pi^{2} \times l}{m T^{2}}$
$=\frac{4 \pi^{2} \times 11.5 \times 10^{-6}}{8.7 \times 10^{-2} \times(0.67)^{2}}$
$=\frac{453.5 \times 10^{-6}}{10^{-2} \times 3.9}=116.28 \times 10^{-4}$
$=0.0116=0.012 \,T$