Q. No.In a certain region of space with volume \(0.2~\text m^3,\) the electric potential is found to be \(5~\text V\) throughout. The magnitude of the electric field in this region is:
1. \(0.5~\text {N/C}\)
2. \(1~\text {N/C}\)
3. \(5~\text {N/C}\)
4. zero
1. \(0.5~\text {N/C}\)
2. \(1~\text {N/C}\)
3. \(5~\text {N/C}\)
4. zero
The plates of a parallel plate capacitor have an area of \(90~\text{cm}^2\) each and are separated by \(2.5~\text{mm}.\) The capacitor is charged by connecting it to a \(400~\text{V}\) supply. How much electrostatic energy is stored by the capacitor?
1. \(1.7\times10^{-6}~\text J\)
2. \(2.12\times10^{-6}~\text J\)
3. \(2.55\times10^{-6}~\text J\)
4. \(1.66\times10^{-6}~\text J\)
A parallel plate air capacitor is charged to potential difference \(V\). After disconnecting the battery, the distance between the plates of the capacitor is increased using an insulating handle. As a result the potential difference between the plates:
| 1. | decreases. | 2. | increases. |
| 3. | becomes zero. | 4. | does not change. |
Some equipotential surfaces are shown in the 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. | can not be defined as \(-\int_{A}^{B} { \vec E\cdot \vec{dl}}\) |
| 2. | must be defined as \(-\int_{A}^{B} {\vec E\cdot \vec{dl}}\) |
| 3. | is zero |
| 4. | can have a non-zero value. |
| a. | in all space |
| b. | for any \(x\) for a given \(z\) |
| c. | for any \(y\) for a given \(z\) |
| d. | on the \(x\text-y\) plane for a given \(z\) |
| 1. | (a), (b), (c) | 2. | (a), (c), (d) |
| 3. | (b), (c), (d) | 4. | (c), (d) |
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 the above statements are correct. |
Two capacitors of capacity \(2~\mu\text{F}\) and \(3~\mu\text{F}\) are charged to the same potential difference of \(6~\text V.\) Now they are connected with opposite polarity as shown. After closing switches \(S_1~\text{and}~S_2\), their final potential difference becomes:
| 1. | \(\text{zero} \) | 2. | \(\frac{4}{3}~\text{V} \) |
| 3. | \(3~\text{V} \) | 4. | \(\frac{6}{5}~\text{V} \) |
The graph of electric potential \((V)\) versus distance \((r)\) is shown in the diagram. The value of the electric field at a distance \(A\) will be:
| 1. | \(5\) V/m | 2. | \(-10\) V/m |
| 3. | \(-5\) V/m | 4. | \(10\) V/m |
An electric dipole of moment \(p\) is placed in an electric field of intensity \(E\). The dipole acquires a position such that the axis of the dipole makes an angle \(\theta\) with the direction of the field. Assuming that the potential energy of the dipole to be zero when \(\theta = 90^{\circ},\) the torque and the potential energy of the dipole will respectively be:
| 1. | \(p E \sin \theta,-p E \cos \theta\) | 2. | \(p E \sin \theta,-2 p E \cos \theta\) |
| 3. | \(p E \sin \theta, 2 p E \cos \theta\) | 4. | \(p E \cos \theta,-p E \sin \theta\) |
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