What is the net flux of the uniform electric field of question 1.15 through a cube of side 20 cm oriented so that its faces are parallel to the coordinate planes?

Solution

Given,

Electric field, \vec{E} = 3 \times 10^{3} \hat{i} {NC}^{- 1}

length of the sides of cube = 20 cm

∴

The area of each face out of the six faces of the cube = 20 x 20 = 400 cm² = 4 x 10^–2 m².

The area vector of four faces of cube ABGH, OBGF, OCDF and ACDH is along +Y axis, –Z axis, –Y axis and +Z axis.
The direction of Electric field is along +X axis.

\vec{∆ S}

is perpendicular to each other so flux through there surfaces are zero.

Hence, the net electric flux through the cube

ϕ = \vec{E} . ∆ \vec{S_{1}} + \vec{E} . ∆ \vec{S_{2}}

Now,

|∆ \vec{S_{1}}| = |∆ \vec{S_{2}}| = 4 \times 10^{- 2} m^{2}

and the angle between

\vec{E} and ∆ \vec{S_{1}}

0 °,

whereas the angle between

\vec{E} and ∆ \vec{S_{2}} is 180 °

Thus,

ϕ = E ∆ S_{1} \cos 0 ° + E ∆ S_{2} \cos 180 ° = E \times 4 \times 10^{- 2} \times 1 + E \times 4 \times 10^{- 2} \times (- 1) = 0

Now, it is established that if some electric flux enters the cube the same amount of flux leaves through the other face, so that the net flux is zero.

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Electric Charges And Fields

What is the net flux of the uniform electric field of question 1.15 through a cube of side 20 cm oriented so that its faces are parallel to the coordinate planes?

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?

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For Daily Free Study Material Join wiredfaculty

Electric Charges And Fields

What is the net flux of the uniform electric field of question 1.15 through a cube of side 20 cm oriented so that its faces are parallel to the coordinate planes?

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?b) Explain why two field lines never cross each other at any point?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?