Four electric charges \(+ q,\) \(+ q,\) \(- q\) and \(- q\) are placed at the corners of a square of side \(2L\) (see figure). The electric potential at point \(A\), mid-way between the two charges \(+ q\) and \(+ q\) is:
1. \(\frac{1}{4 \pi\varepsilon_{0}} \frac{2 q}{L} \left(1 + \frac{1}{\sqrt{5}}\right)\)
2. \(\frac{1}{4 \pi\varepsilon_{0}} \frac{2 q}{L} \left(1 - \frac{1}{\sqrt{5}}\right)\)
3. zero
4. \(\frac{1}{4 \pi \varepsilon_{0}} \frac{2 q}{L} \left(1 + \sqrt{5}\right)\)
A series combination of n1 capacitors, each of value C1, is charged by a source of potential difference 4V. When another parallel combination of n2 capacitors, each of value C2, is charged by a source of potential difference V, it has the same (total) energy stored in it, as the first combination has. The value of C2, in terms of C1, is then:
1.
2.
3.
4.
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. | \(\mathrm{V}_{\mathrm{C}}=\mathrm{V}_B=\mathrm{V}_A\) |
Three capacitors each of capacitance \(C\) and of breakdown voltage \(V\) are joined in series. The capacitance and breakdown voltage of the combination will be:
1.
2.
3.
4. \(3C,~3V\)
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. \(12\pi \varepsilon_0 Q\times 10^{22}~\text{V/m}\)
The energy required to charge a parallel plate condenser of plate separation, \(d\) and plate area of cross-section, \(A\) such that the uniform electric field between the plates is \(E,\) is:
1. | \(\dfrac{\varepsilon_0E^2}{2Ad}\) | 2. | \(\dfrac{\varepsilon_0E^2}{Ad}\) |
3. | \(\varepsilon_0E^2Ad\) | 4. | \(\dfrac{1}{2}\varepsilon_0E^2Ad\) |
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. \({1 \over2}CV^2\)
Charges +q and –q are placed at points A and B, respectively; which are at a distance 2L apart. C is the midpoint between A and B. The work done in moving a charge +Q along the semicircle CRD is:
1.
2.
3.
4.
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. \(pE\)