Q. No.An electric dipole of moment \(\vec {p} \) is lying along a uniform electric field \(\vec{E}.\) The work done in rotating the dipole by \(90^{\circ}\) is:
1. \(\sqrt{2}pE\)
2. \(\dfrac{pE}{2}\)
3. \(2pE\)
4. \(pE\)
1. \(\sqrt{2}pE\)
2. \(\dfrac{pE}{2}\)
3. \(2pE\)
4. \(pE\)
| 1. | \(6\sqrt{5}~\text{N}\) | 2. | \(30~\text{N}\) |
| 3. | \(24~\text{N}\) | 4. | \(4\sqrt{35}~\text{N}\) |
A parallel plate air capacitor of capacitance \(C\) is connected to a cell of emf \(V\) and then disconnected from it. A dielectric slab of dielectric constant \(K,\) which can just fill the air gap of the capacitor is now inserted in it. Which of the following is incorrect?
| 1. | The potential difference between the plates decreases \(K\) times. |
| 2. | The energy stored in the capacitor decreases \(K\) times. |
| 3. | The change in energy stored is \(\frac{1}{2}CV^{2}\left ( \dfrac{1}{K} -1\right ) \) |
| 4. | The charge on the capacitor is not conserved. |
A capacitor of \(2~\mu\text{F}\) is charged as shown in the figure. When the switch \({S}\) is turned to position \(2,\) the percentage of its stored energy dissipated is:
2. \(75\%\)
3. \(80\%\)
4. \(0\%\)
The diagrams below show regions of equipotential.
A positive charge is moved from \(A\) to \(B\) in each diagram. Choose the correct statement from the options given below:
| 1. | in all four cases, the work done is the same. |
| 2. | minimum work is required to move \(q\) in figure \(\mathrm{(a)}.\) |
| 3. | maximum work is required to move \(q\) in figure \(\mathrm{(b)}.\) |
| 4. | maximum work is required to move \(q\) in figure \(\mathrm{(c)}.\) |
In a certain region of space with volume \(0.2~\text m^3,\) the electric potential is found to be \(5~\text V\) throughout. The magnitude of the electric field in this region is:
| 1. | \(0.5~\text {N/C}\) | 2. | \(1~\text {N/C}\) |
| 3. | \(5~\text {N/C}\) | 4. | zero |
Three capacitors connected in series have a capacitance of \(9~\text{pF}\) each. The potential difference across each capacitor if the combination is connected to a \(120~\text V\) supply is:
1. \(10~\text V\)
2. \(20~\text V\)
3. \(30~\text V\)
4. \(40~\text V\)
Three capacitors of capacitances \(2~\text{pF},\) \(3~\text{pF},\) and \(4~\text{pF}\) are connected in parallel. The charge on the \(4~\text{pF}\) capacitor, if the combination is connected to a \(100~\text V\) supply, is:
1. \(4\times10^{-10}~\text C\)
2. \(3\times10^{-9}~\text C\)
3. \(2\times10^{-10}~\text C\)
4. \(1\times10^{-9}~\text C\)
In a parallel plate capacitor with air between the plates, each plate has an area of \(6\times10^{-3}~\text{m}^2,\) and the distance between the plates is \(3~\text{mm}.\) The capacitance of the capacitor is:
1. \(16.12~\text{pF}\)
2. \(17.71~\text{pF}\)
3. \(15.01~\text{pF}\)
4. \(11.32~\text{pF}\)
A \(12~\text{pF}\) capacitor is connected to a \(50~\text V\) battery. How much electrostatic energy is stored in the capacitor?
1. \(3.1\times10^{-8}~\text J\)
2. \(2.9\times10^{-8}~\text J\)
3. \(3.3\times10^{-8}~\text J\)
4. \(1.5\times10^{-8}~\text J\)
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