Question

A metal rod is subjected to cycles of magnetisation at the rate of $42 \,Hz$. Density of the metal is $6 \times 10^{3} \,kg \,m ^{-3}$ and its specific heat capacity is $0.1 \times 10^{3}$ cal $kg { }^{1 \circ} C ^{1}$. If the area of its $B-H$ loop corresponds to energy density of $10^{-2} \,Jm ^{-3}$, then the rise in its temperature in one minute is

• A. $5^{\circ} C$
• B. $10^{\circ} C$
• C. $15^{\circ} C$
• D. $20^{\circ} C$

Answer 1

Answer: (B)

Energy of area of $B-H$ loop,
$\Delta Q=m s(\Delta \theta)$
$\Rightarrow 10^{-2} \times 42 \times 60=6 \times 10^{3} \times 0.1 \times 10^{-3} \times 4.2 \times \Delta \theta$
$\Rightarrow \Delta \theta=\frac{10^{-2} \times 42 \times 60}{6 \times 10^{3} \times 0.1 \times 10^{-3} \times 4.2}$
$\Rightarrow \Delta \theta=10^{\circ} C$