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Question

The electric field in a region is E=5×103x2^i NC1cm1. The charge contained inside a cubical volume bounded by the surfaces x=0,x=1,y=0,y=1,z=0,z=1 is (where x, y, z are in cm) :
  1. 2.21×1012C
  2. 4.42×1012C
  3. 4.42×108C
  4. 2.21×108C

A
2.21×1012C
B
4.42×1012C
C
4.42×108C
D
2.21×108C
Solution
Verified by Toppr

Area of each surfaces a=12cm2=104m2.
As the field is in the direction of x-axis so only surfaces x=0 and x=1 will contribute the flux.
For surface x=0,ϕ0=E.a=5×103×x2.a=5×103×02.a=0
and for x=1,ϕ1=E.a=5×103×x2.a=5×103×12×104=0.25
By Gauss's law, ϕ1=qenϵ0
qen=0.25×8.85×1012=2.21×1012C

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