Assuming the sun to be a spherical body of radius R at a temperature of T K , evaluate the total radiant power incident on Earth at a distance r from - Physics MCQ AIEEE 2006 2026 | ExamTest.live

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Assuming the sun to be a spherical body of radius R at a temperature of T K, evaluate the total radiant power incident on Earth at a distance r from the Sun. (where r_{0} is the radius of the Earth and σ is Stefan’s constant).

Solution & Step-by-step Explanation

Total power radiated by Sun: P = σ (4 π R^{2}) T^{4} .Solar Intensity at distance r : I = \frac{P}{4 π r ^{2}} = \frac{σ 4 π R ^{2} T ^{4}}{4 π r ^{2}} = \frac{σ R ^{2} T ^{4}}{r ^{2}} .Area of Earth that intercepts the radiation: A = π r_{0}^{2} .Total radiant power incident on Earth: W = I \times A = \frac{σ R ^{2} T ^{4}}{r ^{2}} \times π r_{0}^{2} . W = \frac{π r _{0}^{2} R ^{2} σ T ^{4}}{r ^{2}}

Try it yourself before checking the explanation above.

Assuming the sun to be a spherical body of radius R at a temperature of T K, evaluate the total radiant power incident on Earth at a distance r from the Sun. (where r_{0} is the radius of the Earth and σ is Stefan’s constant).

\frac{R ^{2} σ T ^{4}}{r}

\frac{4 π r ^{2} R ^{2} σ T ^{4}}{r _{0}^{2}}

\frac{π r _{0}^{2} R ^{2} σ T ^{4}}{r ^{2}}

\frac{r _{0}^{2} R ^{2} σ T ^{4}}{4 π r ^{2}}

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