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 $6.70s,$ what is the magnitude of the magnetic field?

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

Answer 1

Answer: (A)

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