Question

The sun delivers ${10^3}{\text{ W/}}{{\text{m}}^{\text{2}}}$ of electromagnetic flux to the Earth’s surface. The radiation force on the roof of dimensions ${\text{8m }} \times {\text{ 20m}}$ will be:
(A) $3.33{\text{ }} \times {\text{ 1}}{{\text{0}}^{{\text{ - 5}}}}{\text{ N}}$
(B) $5.33{\text{ }} \times {\text{ 1}}{{\text{0}}^{{\text{ - 4}}}}{\text{ N}}$
(C) $7.33{\text{ }} \times {\text{ 1}}{{\text{0}}^{{\text{ - 3}}}}{\text{ N}}$
(D) $9.33{\text{ }} \times {\text{ 1}}{{\text{0}}^{{\text{ - 2}}}}{\text{ N}}$

Answer 1

Hint: We know that magnetic flux is the number of magnetic field lines that passes through a given closed surface. Basically, the magnetic flux provides a measurement of the total magnetic field passing through a particular surface area. Magnetic field is the product of the perpendicular area through which it penetrates and the average magnetic field strength. With this information, we can easily solve the given question.

Complete step by step answer:
Given in the question,
Let Poynting vector = S = ${10^3}{\text{ W/}}{{\text{m}}^{\text{2}}}$
We know Pressure (P) ${\text{ = }}\dfrac{{\text{S}}}{{\text{c}}}$
Where c is the speed of light.
Therefore,
${\text{P = }}\dfrac{{{\text{1000}}}}{{3 \times {{10}^8}}}$
$ = {\text{ 3.33 }} \times {\text{ }}{10^{ - 6}}{\text{ N/}}{{\text{m}}^{\text{2}}}$
Also, considering the dimensions of the roof, the radiation force on the roof is given as:
$
  {\text{F = P }} \times {\text{ 8 }} \times {\text{ 20}} \\
  {\text{ = 5.33 }} \times {\text{ 1}}{{\text{0}}^{ - 4}}{\text{ N}} \\
 $

Therefore, the correct answer is option B.

Note: Solar constant is the solar flux just outside the atmosphere of the Earth. The reflectance, scattering and absorption of solar light by the Earth’s atmosphere can heavily reduce the solar flux received by approximately 15% to 80% depending on various conditions before the light reaches the surface of the Earth.
We must also keep into consideration the properties of magnetic flux which:
1. Always form a closed loop
2. Always start from north pole and always end in south pole
3. Never intersect each other
4. Are parallel to each other and in the same direction, repel each other
The S.I. The unit of Magnetic flux is Weber (Wb) and its CGS unit is Maxwell.