(a) Definition of electric flux
Stating scalar/ vector
Gauss's Theorem
(b) Explanation of change in electric flux
(a) Electric flux through a given surface is defined as the dot product of electric field and area vector over that surface.
Alternatively
Also accept
Electric flux, through a surface equals the surface integral of the electric field over that surface. ½ It is a scalar quantity
Constructing a cube of side 'd' so that charge 'q' gets placed within of this cube (Gaussian surface ) According to Gauss's law the Electric flux ϕ = Charge enclosed/ɛ0
= q/ɛ0
This is the total flux through all the six faces of the cube
Hence electric flux through the square 1/6 x qɛ0 = q/6ɛ0
(b) If the charge is moved to a distance d and the side of the square is doubled the cube will be constructed to have a side 2d but the total charge enclosed in it will remain the same. Hence the total flux through the cube and therefore the flux through the square will remain the same as before.
[Deduct 1 mark if the student just writes No change /not affected without giving any explanation.]
Detailed Answer
(a) Electric flux : The electric flux linked with a surface is the number of electric lines of force passing through a surface normally and is measured as the surface integral of electric field over that surface, i.e.,
Electric flux ϕ is a scalar quantity. Now calculate the electric flux through the square of side d, we draw a cube of side d such that it completely enclosed the charge q. Now from Gauss’s law
Total flux passing through the cube is given by
(b) If charge is now moved to distance d from centre of square and side of square is doubled, then electric flux is unchanged i.e. remains the same, because electric flux depends only on amount of charge and but not on side of square, OR position of charge.
