Question

define solid angle.show that solid angle subtended by a sphere at its centre is 4pie steradian

$\pi \: sterdian$
​

Answer 1

SOLID ANGLE:

• It is a three dimensional analogue of angle representing the field of view enclosed by an area from a particular point.

• It is a dimensionless quantity.

• It is measured by steradian unit.

Solid Angle attended by a sphere at its centre is 4π:

• Solid angle subtended at the centre can be calculated from the ratio of total surface area by square of the radius.

$\sf{ \therefore \: \Omega = \dfrac{total \: surface \: area}{ {r}^{2} } }$

$\sf{ = > \: \Omega = \dfrac{4\pi {r}^{2} }{ {r}^{2} } }$

$\sf{ = > \: \Omega = 4\pi \: steradian}$

HOPE IT HELPS.

Have a look at the other attachments for detailed information about SOLID ANGLE given by Abhi178 sir.