If \(10^9\) electrons move out of a body to another body every second, how much time approximately is required to get a total charge of \(1\) C on the other body?
1. \(200\) years
2. \(100\) years
3. \(150\) years
4. \(250\) years

The amount of positive and negative charges in a cup of water (\(250\) g) are respectively:

The ratio of the magnitude of electric force to the magnitude of gravitational force for an electron and a proton will be: (\(m_p=1.67\times10^{-27}~\mathrm{kg}\), \(m_e=9.11\times10^{-31}~\mathrm{kg}\))
1. \(2.4\times10^{39}\)
2. \(2.6\times10^{36}\)
3. \(1.4\times10^{36}\)
4. \(1.6\times10^{39}\)

Consider three charges \(q_1,~q_2,~q_3\) each equal to \(q\) at the vertices of an equilateral triangle of side \(l.\) What is the force on a charge \(Q\) (with the same sign as \(q\)) placed at the centroid of the triangle, as shown in the figure?

     
1. \(\frac{3}{4\pi \epsilon _{0}} \frac{Qq}{l^2}\)
2. \(\frac{9}{4\pi \epsilon _{0}} \frac{Qq}{l^2}\)
3. zero
4. \(\frac{6}{4\pi \epsilon _{0}} \frac{Qq}{l^2}\)$\mathrm{}$

Consider the charges \(q,~q,\) and \(-q\) placed at the vertices of an equilateral triangle, as shown in the figure. Then the sum of the forces on the three charges is:

    

1. \(\frac{1}{4\pi \epsilon _{0}}\frac{q^{2}}{l^{2}}\)
2. zero
3. \(\frac{2}{4\pi \epsilon _{0}}\frac{q^{2}}{l^{2}}\)
4. \(\frac{3}{4\pi \epsilon _{0}}\frac{q^{2}}{l^{2}}\)

An electron falls through a distance of \(1.5\) cm in a uniform electric field of magnitude \(2\times10^4\) N/C [figure (a)]. The direction of the field is reversed keeping its magnitude unchanged and a proton falls through the same distance [figure (b)]. If \(t_e\) and \(t_p\) are the time of fall for electron and proton respectively, then:

   
1. \(t_e=t_p\)
2. \(t_e>t_p\)
3. \(t_e<t_p\)
4. none of these$\mathrm{}$

Two charges \(\pm10~\mu\text{C}\) are placed \(5.0\) mm apart. The electric field at a point \(P\) on the axis of the dipole \(15\) cm away from its centre \(O\) on the side of the positive charge, as shown in the figure is:

        
1. \(2.7\times10^5~\text{NC}^{-1}\)
2. \(4.13\times10^6~\text{NC}^{-1}\)
3. \(3.86\times10^6~\text{NC}^{-1}\)
4. \(1.33\times10^5~\text{NC}^{-1}\)

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 accelerations of electron and proton due to the electrical force of their mutual attraction when they are 1 Å (=${10}^{-10} m$) apart are respectively: (\(m_p=1.67\times10^{-27}~\text{kg},~m_e=9.11\times10^{-31}~\text{kg}\))

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