At which latitude, heat gain through insolation approximately equals heat loss through terrestrial radiation -

At which latitude, heat gain through insolation approximately equals heat loss through terrestrial radiation -
A $42\frac{1}{2}^\circ$ North and South
B $22\frac{1}{2}^\circ$ North and South
C $40^\circ$ North and South
D $66^\circ$ North and South

Detailed Solution

The amount of insolation received by the earth decreases from the equator towards the poles, while the heat lost by terrestrial (long-wave) radiation varies much less with latitude.
Between the equator and about $40^\circ$ North and South, the heat gained from insolation exceeds the heat lost by terrestrial radiation, so these regions have a surplus of net radiation.
Beyond about $40^\circ$, towards the poles, the heat lost is more than the heat gained, so these regions have a deficit.
So at about $40^\circ$ North and South the heat gain through insolation approximately equals the heat loss through terrestrial radiation.
The surplus heat of the tropics is carried towards the poles by winds and ocean currents, which keeps the tropics from getting progressively hotter and the poles from getting progressively colder.
Note: the answer key of the source gives $66^\circ$ North and South; it is changed here to $40^\circ$, which is the value given in NCERT geography.

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