Solid angle: The projection of a area divided by r2 (position vector) is called solid angle. The solid angle subtended by an area at a point O is given by Ω = 
.
Where 
is the projection of area.
For sphere the solid angle subtended at the centre is Ω = 
= 
= 
= 
.
Concept on solid angle;
Solid angle subtended at the centre O by the circular section of sphere of radius r (the circular section of sphere creates a cone at centre O with half angle ): Let us consider an elementary ring of radius x thickness dx of the spherical section. The area of that ring is 2
xdx = 
.
The total area of the spherical section is S = 
= 
= 
= 2π 
[1 – cos 
].
The solid angle subtended at the centre by the spherical section is Ω = 
= 2π[1 – cos
].
Concept of electric field lines:
1. Angle of field line with line joining two charges: Two charges +q1 and –q2 are placed at point A and B, respectively. A line of force emerges from +q1 at an angle with the line AB. It terminates at –q2 at angle 
with the line AB. The property of field line is the number of lines of force is proportional to the charge.
For a charge q, the number of field lines per unit solid angle is 
.
The solid angle subtended by the cone of half-angle at point A is 
= 
= the number of lines of force from A within the cone.
Similarly, the solid angle subtended by the cone of half-angle at point B is = 
= 
= the number of lines of force enters at B within the cone.
So, 
= 
Or, 
= 
or, 
= 
.
2. Equation of lines of force: The electric field in a region is 
= axî + byĵ + czk̂. We want to calculate the equation of lines of force for the xy plane, so z = 0.
The component of electric field along x and y axis are Ex = ax and Ey = by.
At any point (x, y) in the plane the slope of lines of force is 
= 
= 
Or, 
= 
Or 
= 
or, In y = 
In x + c.
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