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The total radiant energy per unit area, ...

The total radiant energy per unit area, normal to the direction of incidence, received at a distance `R` from the centre of a star of radius `r` whose outer surface radiates as a black body at a temperature `T K` is given by
(where `sigma` is Stefan's constant)

A

`(sigmar^(2)T^(4))/(R^(2))`

B

`(sigmar^(2)T^(4))/(4pir^(2))`

C

`(sigmar^(4)T^(4))/(r^(4))`

D

`(4pisigmar^(2)T^(4))/(R^(2))`

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Knowledge Check

  • The magnitude of an electric intensity at a point which is at a distance 'r' from the centre of a charged spherical conductor of radius 'R' in terms of the surface charge density 'sigma' is given by 'E' where

    A
    `E=(sigma)/(Kepsi_(0)r^(2))`
    B
    `E=(sigmaR)/(Kepsi_(0)r^(2))`
    C
    `E=(sigmaR^(2))/(Kepsi_(0)r^(2))`
    D
    `E=(sigma^(2)R)/(Kepsi_(0)r^(2))`

  • The sun having surface temperature Ts radiates like a black body. The rasius of sun is Rs and earth is at a distance R from the surface of sun. Earth absorbs radiations falling on its surface from sun only and is at constant temperature T. If radiations falling on earth's surface are alomost parallel and earth also radiates like a blackbody, then

    A
    `T = T_(s) sqrt(R_(s)/(2R))`
    B
    `T = Ts`
    C
    `T = (T_(s))/(2) sqrt((R_(s)/(R ))`
    D
    `T = T_(s) sqrt((R_(s)/(R ))`

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    A
    `0.2sigmaAT^(4)`
    B
    `0.4sigmaAT^(4)`
    C
    `0.6sigmaAT^(4)`
    D
    `0.8sigmaAT^(4)`

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