The electric field in a region is given by 
. The charge contained inside a cubical volume bounded by the surface x = 0, x = 2m, y = 0, y = 2m, z = 0 and z = 2m is nε 0 E 0 . Find the value of n.
Text Solution
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(8)
Sol. Given 
So flux = 
Now total flux = sum of flux through each face
∴ Total flux = 
+ 
+ 
+ 
+ 
+ 
first four terms are = 0, because angle between 
and 
is 90 o so 
. 
= 0
Total flux = 
+ 
For ADEH: 
= E 0 
= E 0 
(0) = 0 [ x = 0]
for BCFG: 
= E 0 x 
= E 0 a 
So, total flux = 0 + 
. ds 
= E 0 a 
= AE 0 a = E 0 a 3 ⇒ ∴ q in = 
= 
= 1.416 × 10
–11 C
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