A metallic sphere of capacitance , charged to electric potential is connected by a metal wire to another metallic sphere of capacitance charged to electric potential . The amount of heat produced in connecting the wire during the process is:
1.
2.
3.
4. zero
1. | \(v\) | 2. | \(v \over \sqrt{2}\) |
3. | \(v \sqrt{2}\) | 4. | \(2v\) |
In the circuit shown in figure, energy stored in \(6~\mu\text{F}\) capacitor will be:
1. | \(48 \times10^{-6}~\text{J}\) | 2. | \(32 \times10^{-6}~\text{J}\) |
3. | \(96 \times10^{-6}~\text{J}\) | 4. | \(24 \times10^{-6}~\text{J}\) |
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 charge \(+q\) is fixed at each of the points ..... infinite, on the \(x\)-axis, and a charge \(-q\) is fixed at each of the points ,..... 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:
1. | is always at +ve potential. |
2. | is always at zero potential. |
3. | is always at negative potential. |
4. | may be at +ve, zero or –ve potential. |
On rotating a point charge having a charge \(q\) around a charge \(Q\) in a circle of radius \(r\), the work done will be:
1. | \(q \times2 \pi r\) | 2. | \(q \times2 \pi Q \over r\) |
3. | zero | 4. | \(Q \over 2\varepsilon_0r\) |
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:
1. | \(K\) | 2. | \(L\) |
3. | \(M\) | 4. | \(N\) |
1. | \(9 \times 10^{-3}~\text{J}\) | 2. | \(9 \times 10^{-3}~\text{eV}\) |
3. | \(2~\text{eV/m}\) | 4. | zero |