29)
since the magnitude of a unit vector is 1 The total flux through the sphere is obtained by adding up flux
through all the different area elements:
FIGURE 1 22 Flux
through a sphere
enclosing a point
charge q at its centre Rationalised 2023-24
30
Physics
2
0
4
all
S
q
S
r
φ
ε
∆
=
Σ
∆
π
Since each area element of the sphere is at the same
distance r from the charge,
2
2
0
4
4
all
S
o
q
q
S
S
r
r
φ
ε
ε
∆
=
Σ ∆
=
π
π
Now S, the total area of the sphere, equals 4pr 2