FIND ELECTRIC FLUX FOR A SPHERE WITH A CONE. FORMULA Q/ EFSILON NOT × ( 1 - COS THETA) .FIND FLUX IF ANGLE IS 60⁰. COS 60⁰=1/2
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Consider Gaussian surface a sphere with its centre at the top and radius, the slant length of cone
Flux through the whole sphere is
ϵ
0
q
Flux through the base of cone =ϕ
e
=(
S
0
S
)×
ϵ
0
q
S
0
= Area of the whole sphere
S= Area of sphere below, base of cone
S
0
=4πR
2
ds=(2πr)Rdr
integration on ds=2πR.2sinθdθ
θ=60
0
S=∫
0
θ
2πR
2
sinθdθ=2πR
2
(1−cosθ)
derives Flux ϕ=(
S
0
S
)×
ϵ
0
q
=
4πR
2
2πR
2
(1−cosθ)
(
ϵ
0
q
)
ϕ=
2ϵ
0
q
(1−cosθ)=
2ϵ
0
q
(1−
2
1
)=
4ϵ
0
q
(∵θ=60
o
)
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