The acceleration of an electron due to the mutual attraction between the electron and a proton when they are \(1.6~\mathring{A}\) apart is:
( \(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9~ \text{Nm}^2 \text{C}^{-2}\) )

Two point charges \(A\) and \(B\), having charges \(+Q\) and \(-Q\) respectively, are placed at a certain distance apart and the force acting between them is \(F.\) If \(25\%\) charge of \(A\) is transferred to \(B\), then the force between the charges becomes:

Suppose the charge of a proton and an electron differ slightly. One of them is \(-e\), the other is (\(e+\Delta e\)). If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance \(d\) (much greater than atomic size) apart is zero, then$$ \(\Delta e\) is of the order of? (Given mass of hydrogen ${\mathrm{}}_{}$\(m_h = 1.67\times 10^{-27}~\text{kg}\)$$)
1. \(10^{-23}~\text{C}\)
2. \(10^{-37}~\text{C}\)
3. \(10^{-47}~\text{C}\)
4. \(10^{-20}~\text{C}\)

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

The unit of permittivity of free space ε₀ is: