A square surface of side \(L\) (m) is in the plane of the paper. A uniform electric field \(\vec{E}\) (V/m), also in the plane of the paper, is limited only to the lower half of the square surface, (see figure). The electric flux in SI units associated with the surface is:     
  

An electric field is uniform, and in the positive \(x\)-direction for positive \(x\), and uniform with the same magnitude but in the negative \(x\)-direction for negative \(x\). It is given that \(\vec{E}=200\hat{i}\) N/C for \(x>0\) and \(\vec{E}=-200\hat{i}\)  N/C for \(x<0\). A right circular cylinder of length \(20~\text{cm}\) and radius \(5~\text{cm}\) has its centre at the origin and its axis along the \(x\text{-}\)axis so that one face is at \(x= + 10~\text{cm}\) and the other is at \(x= -10~\text{cm}\) (as shown in the figure). What is the net outward flux through the cylinder?
        
1. \(0\) 
2. \(1.57~\text{Nm}^2\text{C}^{-1}\)
3. \(3.14~\text{Nm}^2\text{C}^{-1}\)
4. \(2.47~\text{Nm}^2\text{C}^{-1}\)

The electric field in a certain region is acting radially outward and is given by \(E=Ar.\) A charge contained in a sphere of radius \(a\) centered at the origin of the field will be given by:
1. \(4 \pi \varepsilon_{{o}} {A}{a}^2\)
2. \(\varepsilon_{{o}} {A} {a}^2\)
3. \(4 \pi \varepsilon_{{o}} {A} {a}^3\)
4. \(\varepsilon_{{o}} {A}{a}^3\)

If a charge \(Q\) is situated at the corner of a cube, the electric flux passing through all six faces of the cube is:

Two parallel infinite line charges with linear charge densities \(+\lambda\) C/m and \(+\lambda\) C/m are placed at a distance \({R}.\) The electric field mid-way between the two line charges is:
1. \(\frac{\lambda}{2 \pi \varepsilon_0 {R}} \) N/C
2. zero
3. \(\frac{2\lambda}{ \pi \varepsilon_0 {R}} \) N/C
4. \(\frac{\lambda}{ \pi \varepsilon_0 {R}}\) N/C