Question

The sun delivers ${10}^3{\mathrm{Wm}}^{-2}$ of electromagnetic flux on the earth's surface. The total power that is incident on a roof of dimensions $8\mathrm{m}\times 20\mathrm{m}$, is

• A. $6.4\times {10}^3\mathrm{W}$
• B. $3.4\times {10}^4\mathrm{W}$
• C. $1.6\times {10}^5\mathrm{W}$
• D. None of these

Answer 1

The correct option is C

$1.6\times {10}^5\mathrm{W}$

Step 1: Given Data:

Electromagnetic flux, $I={10}^3{\mathrm{Wm}}^{-2}$

Area of the roof, $A=8\mathrm{m}\times 20\mathrm{m}=160{\mathrm{m}}^2$

Step 2: Formula Used:

The power transmitted per unit area, measured on a plane perpendicular to the direction of the energy's transmission, is known as the intensity or flux of radiant energy.

$P=I\times A\dots \dots \dots \dots \dots \left(1\right)$

Where, $P=$Power (flux), $I=$Intensity, $A=$Area

Step 3: Calculation of power incident:

The area of the cross-section of a roof is $A=8\mathrm{m}\times 20\mathrm{m}=160{\mathrm{m}}^2$

Substituting the known values in the above formula in equation (1),

The total power that is incident on a roof of dimensions $8\mathrm{m}\times 20\mathrm{m}$,

$\begin{array}{rcl}P& =& I\times A\\ & =& {10}^3\times 160\\ & =& 160\times {10}^3\\ & =& 1.6\times {10}^5\mathrm{W}\end{array}$

Hence, option C is the correct answer.