Q. No.Three charges \(Q\), \(+q \) and \(+q \) are placed at the vertices of an equilateral triangle of side \(l\) as shown in the figure. If the net electrostatic energy of the system is zero, then \(Q\) is equal to:
| 1. | \(-\frac{q}{2} \) | 2. | \(-q\) |
| 3. | \(+q\) | 4. | \(\text{zero}\) |
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. | \(\frac{1}{2}~\text{V/cm}, 1~\text{V/cm}, 2 ~\text{V/cm} \text { (all along -ve X-axis) }\) |
Four-point charges \(-Q, -q, 2q~\text{and}~2Q\) are placed, one at each corner of the square. The relation between \(Q\) and \(q\) for which the potential at the center of the square is zero is:
| 1. | \(Q= -q\) | 2. | \(Q= -2q\) |
| 3. | \(Q= q\) | 4. | \(Q= 2q\) |
A bullet of mass \(2~\text {gm}\) has a charge of \(2~\mu\text{C}.\) Through what potential difference must it be accelerated, starting from rest, to acquire a speed of \(10~\text{m/s}?\)
1. \(50~\text {kV}\)
2. \(5~\text {V}\)
3. \(50~\text {V}\)
4. \(5~\text {kV}\)
Two identical capacitors \(C_{1}\) and \(C_{2}\) of equal capacitance are connected as shown in the circuit. Terminals \(a\) and \(b\) of the key \(k\) are connected to charge capacitor \(C_{1}\) using a battery of emf \(V\) volt. Now disconnecting \(a\) and \(b\) terminals, terminals \(b\) and \(c\) are connected. Due to this, what will be the percentage loss of energy?
| 1. | \(75\%\) | 2. | \(0\%\) |
| 3. | \(50\%\) | 4. | \(25\%\) |
| 1. | \(V \neq 0 \text { and } \vec{E} \neq 0\) |
| 2. | \(V \neq 0 \text { and } \vec{E}=0\) |
| 3. | \(V=0 \text { and } \vec{E}=0\) |
| 4. | \(V=0 \text { and } \vec{E} \neq 0\) |
| 1. | \(9 \times 10^{-3}~\text{J}\) | 2. | \(9 \times 10^{-3}~\text{eV}\) |
| 3. | \(2~\text{eV/m}\) | 4. | zero |
A conducting sphere of the radius \(R\) is given a charge \(Q.\) The electric potential and the electric field at the centre of the sphere respectively are:
| 1. | zero and \(\frac{Q}{4 \pi \varepsilon_0 {R}^2}\) | 2. | \(\frac{Q}{4 \pi \varepsilon_0 R}\) and zero |
| 3. | \(\frac{Q}{4 \pi \varepsilon_0 R}\) and \(\frac{Q}{4 \pi \varepsilon_0{R}^2}\) | 4. | both are zero |
| 1. | \(8~\text{V/m},\) along the negative \(x\text-\)axis |
| 2. | \(8~\text{V/m},\) along the positive \(x\text-\)axis |
| 3. | \(16~\text{V/m},\) along the negative \(x\text-\)axis |
| 4. | \(16~\text{V/m},\) along the positive \(x\text-\)axis |
A parallel plate air capacitor has capacitance \(C,\) the distance of separation between plates is \(d\) and potential difference \(V\) is applied between the plates. The force of attraction between the plates of the parallel plate air capacitor is:
| 1. | \(\frac{C^2V^2}{2d}\) | 2. | \(\frac{CV^2}{2d}\) |
| 3. | \(\frac{CV^2}{d}\) | 4. | \(\frac{C^2V^2}{2d^2}\) |
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