# Figure shows a ball having a charge $$q$$ fixed at a point $\mathrm{A}$. 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 |
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A ball of mass  and charge ${10}^{–7}$ $\mathrm{C}$ moves from a point $\mathrm{A}$ whose potential is $500$ $\mathrm{V}$ to a point $\mathrm{B}$ whose potential is zero. If the speed of the ball at $\mathrm{A}$ is $0.51$ $\mathrm{m}/\mathrm{s}$, its speed at point $\mathrm{B}$ 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 $1$ $µ\mathrm{F}$ withstands a maximum voltage of 6 kilovolts while another capacitor of $2$ $µ\mathrm{F}$ 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 $$7.5~\mu\text{C}$$. 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.  $\frac{1}{4{\mathrm{\pi \epsilon }}_{0}}\frac{2\mathrm{q}}{\mathrm{L}}\left(1+\frac{1}{\sqrt{5}}\right)$

2.  $\frac{1}{4{\mathrm{\pi \epsilon }}_{0}}\frac{2\mathrm{q}}{\mathrm{L}}\left(1-\frac{1}{\sqrt{5}}\right)$

3.  zero

4.  $\frac{1}{4{\mathrm{\pi \epsilon }}_{0}}\frac{2\mathrm{q}}{\mathrm{L}}\left(1+\sqrt{5}\right)$

Subtopic:  Electric Potential |
73%
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 $\mathrm{\sigma },$ $-\mathrm{\sigma }$, and $\mathrm{\sigma }$ respectively. If ${\mathrm{V}}_{\mathrm{A}},$ ${\mathrm{V}}_{\mathrm{B}}$, and ${\mathrm{V}}_{\mathrm{C}}$ 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 |
83%
From NCERT
AIPMT - 2007
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