In a region, the potential is represented by \(V=(x,y,z)=6x-8xy-8y+6yz,\) where \(V\) is in volts and \(x,y,z\) are in meters. The electric force experienced by a charge of \(2\) coulomb situated at a point \((1,1,1)\) is:
1. \(6\sqrt{5}~\text{N}\)
2. \(30~\text{N}\)
3. \(24~\text{N}\)
4. \(4\sqrt{35}~\text{N}\)
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. \(pE\)
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 \(\frac{1}{2}CV^{2}\left ( \frac{1}{K} -1\right )\) |
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:
The diagrams below show regions of equipotential.
A positive charge is moved from \(\mathrm{A}\) to \(\mathrm{B}\) 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 (a). |
3. | maximum work is required to move \(q\) in figure (b). |
4. | maximum work is required to move \(q\) in figure (c). |
In a certain region of space with volume \(0.2\) m3, the electric potential is found to be \(5\) V throughout. The magnitude of electric field in this region is:
1. \(0.5\) N/C
2. \(1\) N/C
3. \(5\) N/C
4. zero
Three capacitors connected in series have a capacitance of \(9\) pF each. The potential difference across each capacitor if the combination is connected to a \(120\) V supply is:
1. \(10\) V
2. \(20\) V
3. \(30\) V
4. \(40\) V
Three capacitors of capacitances \(2\) pF, \(3\) pF, and \(4\) pF are connected in parallel. The charge on the \(4\) pF capacitor, if the combination is connected to a \(100\) V supply, is:
1. \(4\times10^{-10}\) C
2. \(3\times10^{-9}\) C
3. \(2\times10^{-10}\) C
4. \(1\times10^{-9}\) 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 \(12\) pF capacitor is connected to a \(50\) V battery. How much electrostatic energy is stored in the capacitor?
1. | \(3.1\times10^{-8}\) J | 2. | \(2.9\times10^{-8}\) J |
3. | \(3.3\times10^{-8}\) J | 4. | \(1.5\times10^{-8}\) J |