Question

In an experiment with vibration magneto-meter the value of $4{\pi }^2\frac{I}{T^2}$ for a short bar magnet is observed as $36\times {10}^{-4}$. In the experiment with deflection magnetometer with the same magnet the value of $\frac{4\pi d^3}{2{\mu }_0}$ is observed as $\frac{{10}^8}{36}$. The magnetic moment of the magnet used is :

• A. $50A{m}^2$
• B. $100A{m}^2$
• C. $200A{m}^2$
• D. $1000A{m}^2$

Answer 1

The correct option is B $100A{m}^2$

From first concept $m{B}_H=4{\pi }^2\frac{I}{T^2}$...(i)

and second concept $\frac{m}{B_H}=\frac{4\pi d^3}{2{\mu }_{\circ }}$....(ii)

Multiplying (i) and (ii)

$m^2=$$4{\pi }^2\frac{I}{T^2}$$\times \frac{4\pi d^3}{2{\mu }_{\circ }}$ $36\times {10}^{-4}\times \frac{{10}^8}{32}$

$m=100A{m}^2$