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. \(pE\)
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. \(12\pi \varepsilon_0 Q\times 10^{22}~\text{V/m}\)
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. \(\frac{1}{4 \pi \varepsilon_{0}} \frac{2 q}{L} \left(1 + \sqrt{5}\right)\)
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 |
Three uncharged capacitors of capacities \(C_1, C_2~\text{and}~C_3\) are connected to one another as shown in the figure.
If points A, B, and D, are at potential \(V_1, V_2 ~\text{and}~V_3\) then the potential at O will be:
1. | \(\frac{V_1C_1+V_2C_2+V_3C_3}{C_1+C_2+C_3}\) | 2. | \(\frac{V_1+V_2+V_3}{C_1+C_2+C_3}\) |
3. | \(\frac{V_1(V_2+V_3)}{C_1(C_2+C_3)}\) | 4. | \(\frac{V_1V_2V_3}{C_1C_2C_3}\) |
The figure shows some of the equipotential surfaces. Magnitude and direction of the electric field is given by:
1. | \(200\) V/m, making an angle \(120^\circ\) with the \(x\text-\)axis |
2. | \(100\) V/m, pointing towards the negative \(x\text-\)axis |
3. | \(200\) V/m, making an angle \(60^\circ\) with the \(x\text-\)axis |
4. | \(100\) V/m, making an angle \(30^\circ\) with the \(x\text-\)axis |
In the given figure if \(V = 4~\text{volt}\) each plate of the capacitor has a surface area of\(10^{-2}~\text{m}^2\) and the plates are \(0.1\times10^{-3}~\text{m}\)apart, then the number of excess electrons on the negative plate is:
1. | \(V={p\cos \theta \over 4 \pi \varepsilon_0r^2}\) | 2. | \(V={p\cos \theta \over 4 \pi \varepsilon_0r}\) |
3. | \(V={p\sin \theta \over 4 \pi \varepsilon_0r}\) | 4. | \(V={p\cos \theta \over 2 \pi \varepsilon_0r^2}\) |
Two thin dielectric slabs of dielectric constants \(K_1~\text{and}~K_2(K_{1} < K_{2})\) are inserted between plates of a parallel capacitor, as shown in the figure. The variation of electric field \(E\) between the plates with distance \(d\) as measured from plate \(P\) is correctly shown by:
1. | ![]() |
2. | ![]() |
3. | ![]() |
4. | ![]() |
1. | Zero and \(\mathrm{Q} / 4 \pi \varepsilon_{\mathrm{o}} \mathrm{R}^2\) |
2. | \(\mathrm{Q} / 4 \pi \varepsilon_{\mathrm{O}} \mathrm{R}\) and zero |
3. | \(\mathrm{Q} / 4 \pi \varepsilon_{\mathrm{O}} \mathrm{R}\) and \(\mathrm{Q} / 4 \pi \varepsilon_{\mathrm{o}} \mathrm{R}^2\) |
4. | Both are zero |