Two point charges of $ + 2\,\mu C$ and $ + 6\,\mu C$ repel each other with a force of $12\, N$. If each is given an additional charge of $ - 4\,\mu C$, then force will become

In the circuit shown, a potential difference of $30\, V$ is applied across $AB$ . The potential difference between the points $M$ and $N$ is....$V$

A finite ladder is constructed by connecting several sections of $2\,\mu F$ , $4\,\mu F$ capacitor combinations as shown in the figure. It is terminated by a capacitor of capacitance $C$. What value should be chosen for $C$ such that the equivalent capacitance of the ladder between the points $A$ and $B$ becomes independent of the number of sections in between.......$\mu F$

Two masses $M_1$ and $M_2$ carry positive charges $Q_1$ and $Q_2$, respectively. They are dropped to the floor in a laboratory set up from the same height, where there is a constant electric field vertically upwards. $M_1$ hits the floor before $M_2$. Then,

A hollow insulated conduction sphere is given a positive charge of $10\,\mu C$. What will be the electric field at the centre of the sphere if its radius is $2\,m$ ?................$\mu Cm^{-2}$

Two charges $q_1$ and $q_2$ are placed $30\,cm$ apart, as shown in the figure. A third charge $q_3$ is moved along the arc of a circle of radius $40\,cm$ from $C$ to $D$. The change in the potential energy of the $\frac{{{q_3}}}{{4\pi \,{ \in _0}}}k$ , where $k$ is