Two condensers, one of capacity \(C\) and the other of capacity \(\frac{C}2\) are connected to a \(V\) volt battery, as shown in the figure.
The energy stored in the capacitors when both condensers are fully charged will be:
1. \(2CV^2\)
2. \({1 \over4}CV^2\)
3. \({3 \over4}CV^2\)
4. \({1 \over2}CV^2\)
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. \(\frac{pE}{2}\)
3. \(2pE\)
4. \(pE\)
The electric potential at a point in free space due to a charge \(Q\) coulomb is \(Q\times10^{11}~\text{V}\). The electric field at that point is:
1. \(4\pi \varepsilon_0 Q\times 10^{22}~\text{V/m}\)
2. \(12\pi \varepsilon_0 Q\times 10^{20}~\text{V/m}\)
3. \(4\pi \varepsilon_0 Q\times 10^{20}~\text{V/m}\)
4. \(12\pi \varepsilon_0 Q\times 10^{22}~\text{V/m}\)
Three concentric spherical shells have radii a, b, and c (a<b<c) and have surface charge densities , and respectively. If , and denote the potential of the three shells, and c=a+b, it can be concluded that:
1. | \(\mathrm{V}_{\mathrm{C}}=\mathrm{V}_{\mathrm{A}} \neq \mathrm{V}_{\mathrm{B}}\) |
2. | \(\mathrm{V}_{\mathrm{C}}=\mathrm{V}_B \neq \mathrm{V}_{\mathrm{A}}\) |
3. | \(\mathrm{V}_{\mathrm{C}} \neq \mathrm{V}_B \neq \mathrm{V}_A\) |
4. | \(\mathrm{V}_{\mathrm{C}}=\mathrm{V}_B=\mathrm{V}_A\) |
Four electric charges \(+\mathrm q,\) \(+\mathrm q,\) \(-\mathrm q\) and \(-\mathrm q\) are placed at the corners of a square of side \(2\mathrm{L}\) (see figure). The electric potential at point A, mid-way between the two charges \(+\mathrm q\) and \(+\mathrm q\) is:
1.
2.
3. zero
4.
Maximum charge stored on a metal sphere of radius \(15\) cm may be \(7.5~\mu\text{C}\). The potential energy of the sphere in this case is:
1. \(9.67\) J
2. \(0.25\) J
3. \(3.25\) J
4. \(1.69\) J
The electrostatic force between the metal plates of an isolated parallel plate capacitor \(C\) having a charge \(Q\) and area \(A\) is:
1. | independent of the distance between the plates |
2. | linearly proportional to the distance between the plates |
3. | proportional to the square root of the distance between the plates |
4. | inversely proportional to the distance between the plates |
An electric dipole with dipole moment is placed in an electric field . An external agent turns the dipole slowly until its electric dipole moment becomes . The work done by the external agent is equal to:
1. 4 × 10–28 J
2. –4 × 10–28 J
3. 2.8 × 10–26 J
4. –2.8 × 10–26 J
The variation of potential with distance x from a fixed point is shown in the figure. The electric field at x =13 m is:
1. 7.5 volt/meter
2. –7.5 volt/meter
3. 5 volt/meter
4. –5 volt/meter
In the circuit diagram shown all the capacitors are in\(\mu F\). The equivalent capacitance between points, A & B is (in F):
1. 14/5
2. 7.5
3. 3/7
4. None of these