Assume that you have $10^{23}$ carbon atoms. All the nuclei are placed at the North Pole of the Earth and all the electrons are placed at the South Pole of the Earth. (Radius of Earth = $6400 \ km$). The force between the charges is approximately:

Consider the following charged suspended ball system. If $\alpha < \beta$,then out of the following statements,which can be true at equilibrium? :-
$(a) Q_1 > Q_2, m_1 < m_2$
$(b) Q_1 > Q_2, m_1 > m_2$
$(c) Q_1 < Q_2, m_1 = m_2$
$(d) Q_1 < Q_2, m_1 > m_2$

Two beads,each with charge $q$ and mass $m$,are on a horizontal,frictionless,non-conducting,circular hoop of radius $R$. One of the beads is glued to the hoop at some point,while the other one performs small oscillations about its equilibrium position along the hoop. The square of the angular frequency of the small oscillations is given by [ $\varepsilon_0$ is the permittivity of free space.]

Two point charges $+Q$ and $+q$ repel each other with a force of $100 \,N$. Keeping the distance between them unchanged, if $Q$ is increased by $10 \%$ and $q$ is decreased by $10 \%$, the force of repulsion between them will:

In Millikan's oil drop experiment,an oil drop carrying a charge $Q$ is held stationary by a potential difference of $2400\,V$ between the plates. To keep a drop of half the radius stationary,the potential difference had to be made $600\,V$. What is the charge on the second drop?

Two point charges $+8 q$ and $-2 q$ are located at $x=0$ and $x=L$ respectively. The location of a point on the $x$-axis from the origin,at which the net electric field due to these two point charges is zero is