Figure shows a ball having a charge \(q\) fixed at a point A. Two identical balls having charges \(+q\) and \(–q\) and mass \(‘m’\) each are attached to the ends of a light rod of length \(2 a\)\(2a\). The rod is free to rotate about a fixed axis perpendicular to the plane of the paper and passing through the mid-point of the rod. The system is released from the situation as shown in the figure. The angular velocity of the rod when the rod becomes horizontal will be:

         

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. \(\frac{\sqrt{2} q}{4 \pi \epsilon_0 m a^3} \)

Subtopic:  Electric Potential Energy |
From NCERT
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A ball of mass g and charge 107 C moves from a point A whose potential is 500 V to a point B whose potential is zero. If the speed of the ball at A is 0.51 m/s, its speed at point B will be:

1. 0.6 m / s 2. 6 m / s
3. 2 m / s 4. 4 m / s
Subtopic:  Electric Potential |
 68%
From NCERT
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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. \(\frac{V_1V_2V_3}{C_1C_2C_3}\)

Subtopic:  Combination of Capacitors |
 90%
From NCERT
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A capacitor of 1 µF withstands a maximum voltage of 6 kilovolts while another capacitor of 2 µF 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
Subtopic:  Combination of Capacitors |
 53%
From NCERT
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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
Subtopic:  Capacitance |
 60%
From NCERT
NEET - 2018
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Maximum charge stored on a metal sphere of radius 15 cm may be 7.5 μC. 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

Subtopic:  Energy stored in Capacitor |
 53%
From NCERT
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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.  14πε02qL1+15

2.  14πε02qL1-15

3.  zero

4.  14πε02qL1+5

Subtopic:  Electric Potential |
 74%
From NCERT
AIPMT - 2011
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Three concentric spherical shells have radii a, b, and c (a<b<c) and have surface charge densities σ, -σ, and σ respectively. If VA, VB, and VC 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. \(\mathrm{V}_{\mathrm{C}}=\mathrm{V}_B=\mathrm{V}_A\)

Subtopic:  Electric Potential |
From NCERT
AIPMT - 2009
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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. \(12\pi \varepsilon_0 Q\times 10^{22}~\text{V/m}\)

Subtopic:  Relation between Field & Potential |
 72%
From NCERT
AIPMT - 2008
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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. \({1 \over2}CV^2\)

Subtopic:  Energy stored in Capacitor |
 84%
From NCERT
AIPMT - 2007
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