A hollow conducting sphere is placed in an electric field produced by a point charge placed at \(P\) as shown in the figure. Let\(​​V_A ~,V_B~,V_C\) be the potentials at points \(A\), \(B\) and \(C\) respectively. Then:

        
1. \(V_A<V_B<V_C\)
2. \(V_A>V_B>V_C\)
3. \(V_C>V_B=V_A\)
4. \(V_A=V_B=V_C\)

A metallic sphere of capacitance $C_1$, charged to electric potential $V_1$ is connected by a metal wire to another metallic sphere of capacitance $C_2$ charged to electric potential $V_2$. The amount of heat produced in connecting the wire during the process is:

1.$\frac{C_1{C}_2}{2\left(C_1+C_2\right)}{\left(V_1+V_2\right)}^2$

2. $\frac{C_1{C}_2}{2(C_1+C_2)}{(V_1-V_2)}^2$

3. $\frac{C_1{C}_2}{C_1+C_2}{(V_1-V_2)}^2$

4. zero

In the circuit shown in the figure, the energy stored in \(6~\mu\text{F}\) capacitor will be:
      

A charge \(+q\) is fixed at each of the points $x=x_0,$ $x=3x_0,$ $x=5x_0$ ..... infinite, on the \(x\)-axis, and a charge \(-q\) is fixed at each of the points $x=2x_0,$ $x=4x_0,x=6x_0$,..... infinite. Here \(x_0\) is a positive constant. Take the electric potential at a point due to a charge \(Q\) at a distance \(r\) from it to be \(\frac{Q}{4\pi \varepsilon_0 r}\). Then, the potential at the origin due to the above system of charges is:
1. \(0\)
2. \(\frac{q}{8 \pi \varepsilon_{0} x_{0} \mathrm{ln} 2}\)
3. \(\infty\)
4. \(\frac{q \mathrm{ln} 2}{4 \pi \varepsilon_{0} x_{0}}\)

A conductor with a positive charge:

On rotating a point charge having a charge \(q\) around a charge \(Q\) in a circle of radius \(r,\) the work done will be:

In the figure the charge \(Q\) is at the centre of the circle. Work done by the conservative force is maximum when another charge is taken from point \(P\) to: