Question

A magnetic needle has magnetic moment $6.7\times 10^{-2}$ $A{m}^2$ and moment of inertia $=7.5\times 10^{-6}kg{m}^2.$ If it performs 10 complete oscillations in 6.70 sec. What is the magnitude of magnetic field?

• A. $9.89\times 10^{-2}T$
• B. $9.852\times 10^{-3}T$
• C. $10\times 10^{-5}T$
• D. $12T$

Answer 1

Answer: (B)

As we know $T=2\pi \sqrt{\frac{I}{MB}}$
$B=4{\pi }^2\times \frac{I}{M{T}^2}$
$=4\times \frac{22}{7}\times \frac{22}{7}\times \frac{7.5\times 10^{-6}}{6.7\times 10^{-2}\times (0.67{)}^2}$
$=4\times {\left(\frac{22}{7}\right)}^2\times \frac{7.5\times 10^{-6}}{6.7\times 10^{-2}\times (0.67{)}^2}$
$B=9.852\times 10^{-3}T$