The arc $AB$ with the centre $C$ and the infinitely long wire having linear charge density $\mathrm{\lambda }$ are lying in the same plane. The minimum amount of work to be done to move a point charge $q_0$ from point $A$ to $B$ through a circular path $AB$ of radius $a$ is equal to

A charged block is projected on a rough horizontal surface with speed $v_0$. The value of coefficient of friction if the kinetic energy of the block remains constant is

Three charges $Q,+q$ and $+q$ are placed at the vertices of a right angled isosceles triangle as shown in figure. The net electrostatics energy of the configuration is zero if $Q$ is equal to

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

If linear charge density of a bent wire as shown in the figure is $\mathrm{\lambda }$. Then.