Figure shows a ball having a charge \(q\) fixed at a point . Two identical balls having charges \(+q\) and \(–q\) and mass \(‘m’\) each are attached to the ends of a light rod of length \(2 a\)
1. | \(\frac{\sqrt{2} \mathrm{q}}{3 \pi \epsilon_0 \mathrm{ma}^3} \) | 2. | \(\frac{\mathrm{q}}{\sqrt{3 \pi \epsilon_0 \mathrm{ma}^3 }}\) |
3. | \(\frac{\mathrm{q}}{\sqrt{6 \pi \epsilon_0 \mathrm{ma}^3 }} \) | 4. | \(\frac{\sqrt{2} q}{4 \pi \epsilon_0 m a^3} \) |
A ball of mass and charge moves from a point whose potential is to a point whose potential is zero. If the speed of the ball at is , its speed at point will be:
1. | 0.6 m / s | 2. | 6 m / s |
3. | 2 m / s | 4. | 4 m / s |
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 \(\mathrm{A}\), \(\mathrm{B}\), and \(\mathrm{D}\), are at potential \(V_1, V_2 ~\text{and}~V_3\) then the potential at \(\mathrm{O}\) 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. \(\frac{V_1V_2V_3}{C_1C_2C_3}\)
A capacitor of withstands a maximum voltage of 6 kilovolts while another capacitor of withstands a maximum voltage of 4 kilovolts. If the two capacitors are connected in series, the system will withstand a maximum voltage of:
1. | 2 kV | 2. | 4 kV |
3. | 6 kV | 4. | 9 kV |
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. |
Maximum charge stored on a metal sphere of radius 15 cm may be . 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
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.
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. | \(\mathrm{V}_{\mathrm{C}}=\mathrm{V}_B=\mathrm{V}_A\) |
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. \(12\pi \varepsilon_0 Q\times 10^{22}~\text{V/m}\)
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. \({1 \over2}CV^2\)