electric field in a given region of space is E=5xi+6yj+3zk. find the volume charge density?
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The electric flux will contribute only due to surfaces x=0 and x=a because the electric filed is perpendicular to other surfaces.
Thus, ϕ(x=0)=
l
E
0
(0)
.a
2
=0 and ϕ(x=a)=
l
E
0
(a)
.a
2
=
l
E
0
.a
3
using Gauss's law,
ϵ
0
q
=ϕ(x=a)=
l
E
0
.a
3
⇒q=
l
E
0
.a
3
ϵ
0
=
2×10
−2
5×10
3
×
×10
−6
×8.854×10
−12
=2.21×10
−12
∼2×10
−12
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