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Question

A cube has sides of length L = 0.300 𝑚. It is placed with one corner at the origin as shown in the
figure. The electric field is not uniform, but it is given by E=(5.00NC1)x^i+(3.00 NC1)z^k.


The surfaces that have zero flux are

A
S2,S4 and S5
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B
S1,S3,S4 and S6
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C
S1,S2 and S3
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D
S2,S3 and S4
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Solution

The correct option is B S1,S3,S4 and S6
For surface z=0 on xy plane,
Normal S4=l2(^k)

For surface z=l on xy plane,
Normal S2=l2(^k)

For surface x=0 on yz plane,
Normal S6=l2(^i)

For surface x=l on yz plane,
Normal S5=l2(^i)

For surface y=0 on xz plane,
Normal S1=l2(^j)

For surface y=l on xy plane,
Normal S3=l2(^j)

Electric field E=5x^i+3z^k
Flux ϕ=E.A

ϕ4=3l2z=0
ϕ2=3zl2=3l3
ϕ6=5l2x=0
ϕ5=5l2x=5l3
ϕ1=0
ϕ3=0

So the surfaces which have zero flux are S1,S3,S4 and S6.

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