The insulation property of air breaks down at \(E = 3\times 10^{6}~\text{V/m}\). The maximum charge that can be given to a sphere of diameter \(5\) m is approximately:
1. \(2\times 10^{-5}~\text{C}\)
2. \(2\times 10^{-4}~\text{C}\)
3. \(2\times 10^{-3}~\text{C}\)
4. \(3\times 10^{-3}~\text{C}\)
The dielectric constant of pure water is \(81\). Its permittivity will be: (in MKS units)
1. \(1.02\times 10^{-13}\)
2. \(8.86\times 10^{-12}\)
3. \(7.17\times 10^{-10}\)
4. \(7.8\times 10^{-10}\)
In a circuit, \(5\) C of charge is passed through a battery in a given time. The plates of the battery are maintained at a potential difference of \(12\) V. The work done by the battery is:
1. | \(120\) J | 2. | \(60\) J |
3. | \(30\) J | 4. | \(15\) J |
Some equipotential surfaces are shown in figure. The electric field at points \(A\), \(B\) and \(C\) are respectively:
1. | \(1~\text{V/cm}, \frac{1}{2} ~\text{V/cm}, 2~\text{V/cm} \text { (all along +ve X-axis) }\) |
2. | \(1~\text{V/cm}, \frac{1}{2} ~\text{V/cm}, 2 ~\text{V/cm} \text { (all along -ve X-axis) }\) |
3. | \(\frac{1}{2} ~\text{V/cm}, 1~\text{V/cm}, 2 ~\text{V/cm} \text { (all along +ve X-axis) }\) |
4. | \(\frac{1}{2}~\text{V/cm}, 1~\text{V/cm}, 2 ~\text{V/cm} \text { (all along -ve X-axis) }\) |
1. | plane parallel to \(yz\) plane |
2. | plane parallel to the \(x\text{-}\)axis |
3. | concentric circle centered at the origin |
4. | coaxial cylinder with axis parallel to the \(y\text-\)axis |
A circuit has section \(AB\) as shown in figure. The emf of the cell is \(10\) V. The potential difference \(V_{AB}= 5~\text{V}\). The charge on the capacitor \(C_1\) is:
1. | \(10~\mu\text{C}\) | 2. | \(5~\mu\text{C}\) |
3. | \(15~\mu\text{C}\) | 4. | Can't be determine |
A charge \(q_1=5 \times 10^{-8} ~\text{C}\) is kept at \(3\) cm from a charge \(q_2=-2 \times 10^{-8} ~\text{C}\). The potential energy of the system relative to the potential energy at infinite separation is:
1. | \(3\times 10^{-4}~\text{J}\) | 2. | \(-3\times 10^{-4}~\text{J}\) |
3. | \(9\times 10^{-6}~\text{J}\) | 4. | \(-9\times 10^{-6}~\text{J}\) |
Which of the following statements is correct regarding the electrostatics of conductors?
1. | The interior of the conductor with no cavity can have no excess charge in the static situation. |
2. | The electrostatic potential is constant throughout the volume of the conductor. |
3. | The electrostatic potential has the same value inside as that on its surface. |
4. | All of these. |
A positive charge \(q\) and a negative charge \(-q\) are placed at \(x=-a\) and \(x=+a\) respectively. The variation of \(V\) along \(x\text-\)axis is represented by the graph:
1. | 2. | ||
3. | 4. |
1. | \(16\) | 2. | \(8\) |
3. | \(64\) | 4. | \(32\) |