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(A) According to the Stefan-Boltzmann law,the total power radiated by a black body of surface area $A$ at temperature $T$ is given by $P = A \sigma T^

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$\frac{\sigma r^2 T^4}{R^2}$

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(A) According to the Stefan-Boltzmann law,the total power radiated by a black body of surface area $A$ at temperature $T$ is given by $P = A \sigma T^4$.For a spherical star of radius $r$,the surface area is $A = 4 \pi r^2$.Thus,the total power radiated by the star is $P = (4 \pi r^2) \sigma T^4$.This power is distributed uniformly over a spherical surface of radius $R$ at a distance $R$ from the center of the star.The intensity $I$ (radiant energy per unit area per unit time) at distance $R$ is given by $I = \frac{P}{4 \pi R^2}$.Substituting the value of $P$,we get $I = \frac{4 \pi r^2 \sigma T^4}{4 \pi R^2} = \frac{\sigma r^2 T^4}{R^2}$.

The outer surface of a star in the form of a sphere radiates heat as a black body at temperature $T$. The total radiant energy per unit area,normal to the direction of incidence,received at a distance $R$ from the center of a star of radius $r$ is $(R > r)$ ($\sigma =$ Stefan's constant).

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