91影视

• Mass of the sheet is$m$
• Face area of the sheet is$A$
• Specific heat of the sheet is$c_s$
• Maximum electric field of wave is$E_m$

By using the concept of specific heat, the intensity of the electromagnetic wave, and the rate of flow of energy, we will find the rate of increase in temperature.

Formulae:

The absorbed heat by the body due to specific heat,$Q=c_{s}m螖T鈰�鈰�鈰�鈰�鈰�鈰�\left(1\right)$

The intensity of the wave due to electric field,$I=\frac{1}{2c{渭}_0}{E}_m^2鈰�鈰�鈰�鈰�鈰�鈰�\left(2\right)$

The rate of energy absorption by the body,$P=\frac{dE}{dt}=IA鈰�鈰�鈰�鈰�鈰�鈰�\left(3\right)$

Substituting the intensity value of equation (2) in equation (3), the rate of energy can be given as follows:

$\frac{dE}{dt}=\frac{1}{2C{渭}_0}{E}_m^{2}A$

Inthegiven problem, electric field energy is transferred as heat energy. Thus, we can write that

$\begin{array}{c}\frac{dQ}{dt}=\frac{dE}{dt}\\ =\frac{1}{2C{渭}_0}{E}_m^{2}A鈰�鈰�鈰�鈰�鈰�鈰�\left(4\right)\end{array}$

$\begin{array}{c}\frac{dQ}{dt}=c_{s}m\frac{dT}{dt}\\ \frac{dT}{dt}=\frac{1}{c_{s}m}\frac{dQ}{dt}\\ =\frac{1}{c_{s}m}\frac{1}{2c{渭}_0}{E}_m^{2}A\left(\text{fromequation(4)}\right)\\ =\frac{1}{2c{渭}_0{c}_{s}m}{E}_m^{2}A\end{array}$

Hence, the rate at which the sheet鈥檚 temperature increases due to the absorption of the wave is.$\frac{1}{2c{渭}_0{c}_{s}m}{E}_m^{2}A$