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Question
The cube as shown in Fig. has sides of length L=10.0 cm. The electric field is uniform, has a magnitude E=4.00×103NC−1, and is parallel to the xy−plane at an angle of 37∘ measured from the +x−axis towards the +y−axis.
The surfaces that have zero flux are
The cube as shown in Fig. has sides of length L=10.0 cm. The electric field is uniform, has a magnitude E=4.00×103NC−1, and is parallel to the xy−plane at an angle of 37∘ measured from the +x−axis towards the +y−axis.
The surfaces that have zero flux are
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Solution
The correct option is C S2 and S4
Φ=→E⋅→A=EAcosθ, where, →A=A^n
^nS1=−^j(left),ΦS1=−(4×103NC−1(0.1 m)2cos(90∘−37∘)
=−24 Nm2C−1
^nS2=+^k(top),
ΦS2=−(4×103NC−1)(0.1 m)2cos(90∘−37∘)
=+24 Nm2C−1
^nS4=−^k(bottom),
ΦS4=(4×103NC−1)(0.1 m)2cos90∘=0
^nS5=+^i(front),
ΦS5=+(4×103NC−1)(0.1 m)2cos37∘=32 Nm2C−1
^nS5=−^i(back),
ΦS6=−(4×103×103NC−1)(0.1 m)2cos37∘=−32 Nm2C−1
As the field is uniform, so the total through the cube must be zero; any flux entering the cube must also leave it.
Φ=→E⋅→A=EAcosθ, where, →A=A^n
^nS1=−^j(left),ΦS1=−(4×103NC−1(0.1 m)2cos(90∘−37∘)
=−24 Nm2C−1
^nS2=+^k(top),
ΦS2=−(4×103NC−1)(0.1 m)2cos(90∘−37∘)
=+24 Nm2C−1
^nS4=−^k(bottom),
ΦS4=(4×103NC−1)(0.1 m)2cos90∘=0
^nS5=+^i(front),
ΦS5=+(4×103NC−1)(0.1 m)2cos37∘=32 Nm2C−1
^nS5=−^i(back),
ΦS6=−(4×103×103NC−1)(0.1 m)2cos37∘=−32 Nm2C−1
As the field is uniform, so the total through the cube must be zero; any flux entering the cube must also leave it.
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