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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

`(sigma r^(2) T^(4))/(R^(2))`

B

`(sigma r^(2)T^(4))/(4pi r^(2))`

C

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

D

`(4pi sigma r^(2) T^(4))/(R^(2))`

Text Solution

Verified by Experts

The correct Answer is:
A
According to the Stefan Boltzmann law, the power radiated by the star whose outer surface radiates as a black body at temperature TK is given by
`P rho = sigma 4pi r^(2) T^(4)`
where, r= radius of the star `sigma` Stefan.s constant
The radiant power per unit area received at a distance R from the centre of a star is `S= (P)/(4pi R^(2)) = (sigma 4pi r^(2)T^(4))/(4pi R^(2)) = (sigma r^(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))`
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    A
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