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. \(4 \pi \varepsilon_{\mathrm{o}} \mathrm{A} \mathrm{a}^2\)
2. \(\varepsilon_{\mathrm{o}} \mathrm{A} \mathrm{a}^2\)
3. \(4 \pi \varepsilon_{\mathrm{o}} \mathrm{A} \mathrm{a}^3\)
4. \(\varepsilon_{\mathrm{o}} \mathrm{A} \mathrm{a}^3\)

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

2. $\frac{q}{8{\epsilon }_o}$

3. $\frac{q}{{\epsilon }_o}$

4. $\frac{q}{2{\epsilon }_o}$

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)

1. $\frac{4\pi {\epsilon }_{0}F{d}^2}{e^2}$

2. $\sqrt{\frac{4\pi {\epsilon }_{0}F{d}^2}{d^2}}$

3. $\sqrt{\frac{4\pi {\epsilon }_{0}F{d}^2}{e^2}}$

4. $\frac{4\pi {\epsilon }_{0}F{d}^2}{q^2}$

A square surface of side \(L\) (metre) in the plane of the paper is placed in a uniform electric field \(E\) (volt/m) acting along the same plane at an angle θ with the horizontal side of the square as shown in the figure. The electric flux linked to the surface in the unit of V-m is:
     

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