A metal rod is subjected to cycles of magnetisation at the rate of $42 \mathrm{~Hz}$. Density of the metal is $6 imes 10^3 \mathrm{~kg} \mathrm{~m}^{-3}$ and its specific heat capacity is $0.1 imes 10^{-3} \mathrm{cal} \mathrm{kg}^{-1}{ }^{\circ} \mathrm{C}^{-1}$. If the area of its $B-H$ loop…

Question

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

Aicharya · Accepted Answer

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

A metal rod is subjected to cycles of magnetisation at the rate of $42 \mathrm{~Hz}$. Density of the metal…

Solution