Q. No.Two tiny spheres carrying charges of \(1.5\) µC and \(2.5\) µC are located \(30\) cm apart. What is the potential at a point \(10\) cm from the midpoint in a plane normal to the line and passing through the mid-point?
1.
\(1.5\times 10^{5}\) V
2.
\(1.0\times 10^{5}\) V
3.
\(2.4\times 10^{5}\) V
4.
\(2.0\times 10^{5}\) V
A \(12~\text{pF}\) capacitor is connected to a \(50~\text V\) battery. How much electrostatic energy is stored in the capacitor?
1. \(3.1\times10^{-8}~\text J\)
2. \(2.9\times10^{-8}~\text J\)
3. \(3.3\times10^{-8}~\text J\)
4. \(1.5\times10^{-8}~\text J\)
In a parallel plate capacitor with air between the plates, each plate has an area of \(6\times10^{-3}~\text{m}^2,\) and the distance between the plates is \(3~\text{mm}.\) The capacitance of the capacitor is:
1. \(16.12~\text{pF}\)
2. \(17.71~\text{pF}\)
3. \(15.01~\text{pF}\)
4. \(11.32~\text{pF}\)
Three capacitors of capacitances \(2~\text{pF},\) \(3~\text{pF},\) and \(4~\text{pF}\) are connected in parallel. The charge on the \(4~\text{pF}\) capacitor, if the combination is connected to a \(100~\text V\) supply, is:
1. \(4\times10^{-10}~\text C\)
2. \(3\times10^{-9}~\text C\)
3. \(2\times10^{-10}~\text C\)
4. \(1\times10^{-9}~\text C\)
Three capacitors connected in series have a capacitance of \(9~\text{pF}\) each. The potential difference across each capacitor if the combination is connected to a \(120~\text V\) supply is:
1. \(10~\text V\)
2. \(20~\text V\)
3. \(30~\text V\)
4. \(40~\text V\)
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
Consider a uniform electric field in the \(z\text-\)direction. The potential is a constant:
| (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 \( z.\) |
Choose the correct from the given options:
| 1. | (c) and (d) only | 2. | (a) and (c) only |
| 3. | (b), (c) and (d) only | 4. | (a) and (b) only |
| Statement I: | At any point inside the sphere, electric intensity is zero. |
| Statement II: | At any point inside the sphere, the electrostatic potential is \(100~\text{V}.\) |
Which of the following is a correct statement?
| 1. | Statement I is True but Statement II is False. |
| 2. | Both Statement I and Statement II are False. |
| 3. | Statement I is True, Statement II is also True and Statement I is the cause of Statement II. |
| 4. | Statement I is True, Statement II is also True but the statements are independent. |
As per this diagram, a point charge \(+q\) is placed at the origin \(O.\) Work done in taking another point charge \(-Q\) from the point \(A,\) coordinates \((0,a),\) to another point \(B,\) coordinates \((a,0),\) along the straight path \(AB\) is:
| 1. | \( \left(\dfrac{-{qQ}}{4 \pi \varepsilon_0} \dfrac{1}{{a}^2}\right) \sqrt{2} {a}\) | 2. | zero |
| 3. | \( \left(\dfrac{qQ}{4 \pi \varepsilon_0} \dfrac{1}{{a}^2}\right) \dfrac{1}{\sqrt{2}} \) | 4. | \( \left(\dfrac{{qQ}}{4 \pi \varepsilon_0} \dfrac{1}{{a}^2}\right) \sqrt{2} {a}\) |
Some charge is being given to a conductor. Then it's potential:
| 1. | is maximum at the surface. |
| 2. | is maximum at the centre. |
| 3. | remains the same throughout the conductor. |
| 4. | is maximum somewhere between the surface and the centre. |
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