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:

A sphere encloses an electric dipole with charges \(\pm3\times10^{-6}\) C. What is the total electric flux through the sphere?
1. \(-3\times10^{-6}\) N-m²/C
2. zero
3. \(3\times10^{-6}\) N-m²/C
4. \(6\times10^{-6}\) N-m²/C

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. \(\varepsilon_{{o}} {A}{a}^3\)

What is the flux through a cube of side \(a,\) if a point charge of \(q\) is placed at one of its corners?
1. \(\frac{2q}{\varepsilon_0}\)
2. \(\frac{q}{8\varepsilon_0}\)
3. \(\frac{q}{\varepsilon_0}\)
4. \(\frac{q}{2\varepsilon_0}\)

The electric field at a distance \(\frac{3R}{2}\) from the centre of a charged conducting spherical shell of radius \(R\) is \(E\). The electric field at a distance \(\frac{R}{2}\) from the centre of the sphere is:
1. \(E\)
2. \(\frac{E}{2}\)
3. \(\frac{E}{3}\)
4. zero