Steradian// solid angle for Class XI (2020)

[@anwarsiraj4994]

Correction: 1 steradian is the solid angle subtended at the centre of sphere by an area of its surface equal to the square of the radius of that sphere

[@hrqasim]

Ustad-E_Muhtram, that is "1" steradian. Steradian is the angle subtended at the center of a sphere by some area at the surface of that sphere(need not be equal to r^2).

[@anwarsiraj4994]

@@hrqasim you want to say any area at the surface of sphere?

[@hrqasim]

@@anwarsiraj4994 Yes Exactly

[@anwarsiraj4994]

@@hrqasim No

[@anwarsiraj4994]

@@hrqasim. The steradian (symbolized sr) is the Standard International (SI) unit of solid angular measure. There are 4 pi, or approximately 12.5664, steradians in a complete sphere. A steradian is defined as conical in shape, as shown in the illustration. Point P represents the center of the sphere. The solid (conical) angle q, representing one steradian, is such that the area A of the subtended portion of the sphere is equal to r2, where r is the radius of the sphere. A general sense of the steradian can be envisioned by considering a sphere whose radius is one meter (r = 1m). Imagine a cone with its apex P at the center of the sphere, and that intersects the surface in a circle (shown as a red ellipse, the upper half of which is dashed). Suppose the flare angle q of the cone is such that the area A of the spherical segment within the circle is equal to one meter squared (A = 1 m2). Then the flare angle of the cone is equal to 1 steradian (q = 1 sr). The total surface area of the sphere is, in this case, 12.5664 square meters (4 pi times the square of the radius). Based on the foregoing example, the geometry of which is independent of scale, it can be said that a solid angle of 1 sr encompasses about 1/12.5664, or 7.9577 percent, of the space surrounding a point. The number of steradians in a given solid angle can be determined by dividing the area on the surface of a sphere lying within the intersection of that solid angle with the surface of the sphere (when the focus of the solid angle is located at the center of the sphere) by the square of the radius of the sphere. Also see radian and Standard International (SI) System of Units.

[@lailakhan6392]

damn i missed this chap in clg but now alhmdulillah im totally satisfied with it Thanks sir May Allah give u Ajr💫

[@basmaahmed7327]

Very nicely explained 👏

[@lutfullahsherani8725]

Thank you sir , I cleared my concept about this topic.

[@blacklist7576]

Thanks sir for this video God bless you ❤️

[@Factcheckpk]

sir how 4pi r square is derived

[@muhammadejaz4663]

Aoa.sir, steradian is defined as the solid angle subtended at the centre of sphere by an area of its surface equal to the square of the radius of that sphere.

[@anwarsiraj4994]

Yes I made a mistake Thank you for correction

[@qalamtv4710]

No problem sir Great professors can have small mistakes Keep it up