Two parallel infinite line charges with linear charge densities \(+\lambda~\text{C/m}\) and \(+\lambda~\text{C/m}\) are placed at a distance \({R}.\) The electric field mid-way between the two line charges is:

1.	\(\frac{\lambda}{2 \pi \varepsilon_0 {R}}~\text{N/C}\)	2.	zero
3.	\(\frac{2\lambda}{ \pi \varepsilon_0 {R}} ~\text{N/C}\)	4.	\(\frac{\lambda}{ \pi \varepsilon_0 {R}}~\text{N/C}\)

An isolated sphere of radius \(R\) contains a uniform volume distribution of positive charge. Which of the curve on the graph below correctly illustrates the dependence of the magnitude of the electric field of the sphere as a function of the distance \(r\) from its centre?
                
1. A 
2. B
3. C 
4. D

A square surface of a side \(L\) \(\text{(m)}\) is in the plane of the paper. A uniform electric field \(\vec{E}\) \(\text{(V/m)},\) 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:     
  

A hollow cylinder has a charge \(q\) coulomb within it (at the geometrical centre). If \(\phi\) is the electric flux in units of Volt-meter associated with the curved surface \(B,\) the flux linked with the plane surface \(A\) in units of volt-meter will be: 
           
1. \(\frac{1}{2}\left(\frac{q}{\varepsilon_0}-\phi\right)\)
2. \(\frac{q}{2\varepsilon_0}\)
3. \(\frac{\phi}{3}\)
4. \(\frac{q}{\varepsilon_0}-\phi\)

Three-point charges \(+q\), \(-2q\) and \(+q\) are placed at points \((x=0,y=a,z=0)\), \((x=0, y=0,z=0)\) and \((x=a, y=0, z=0)\), respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are:

A thin conducting ring of the radius \(R\) is given a charge \(+Q.\) The electric field at the centre \(O\) of the ring due to the charge on the part \(AKB\) of the ring is \(E.\) The electric field at the centre due to the charge on the part \(ACDB\) of the ring is:
              

Two positive ions, each carrying a charge \(q\), are separated by a distance \(d\). If \(F\) is the force of repulsion between the ions, the number of electrons missing from each ion will be:
(\(e\) is the charge on an electron)

What is the flux through a cube of side \(a,\) if a point charge of \(q\) is placed at one of its corners?