# Two metal spheres, one of radius $$R$$ and the other of radius $$2R$$ respectively have the same surface charge density $$\sigma.$$ They are brought in contact and separated.  What will be the new surface charge densities on them? 1. $$\sigma_{1}=\frac{5}{6}\sigma ,~\sigma_{2}=\frac{5}{6}\sigma$$ 2. $$\sigma_{1}=\frac{5}{2}\sigma ,~\sigma_{2}=\frac{5}{6}\sigma$$ 3. $$\sigma_{1}=\frac{5}{2}\sigma ,~\sigma_{2}=\frac{5}{3}\sigma$$ 4. $$\sigma_{1}=\frac{5}{3}\sigma ,~\sigma_{2}=\frac{5}{6}\sigma$$

Subtopic:  Electric Potential |
55%
From NCERT
NEET - 2019
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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. $$25\%$$

Subtopic:  Energy stored in Capacitor |
63%
From NCERT
NEET - 2019
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A parallel plate air capacitor is charged to a potential difference of V volts. After disconnecting the charging 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. does not change.

3. becomes zero.

4. increases.

Subtopic:  Capacitance |
56%
From NCERT
AIPMT - 2006
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An electric dipole of moment $$\vec {p}$$ is lying along a uniform electric field $$\vec{E}$$. The work done in rotating the dipole by $$90^{\circ}$$ is:
1. $$\sqrt{2}pE$$
2. $$\frac{pE}{2}$$
3. $$2pE$$
4. $$pE$$

Subtopic:  Energy of Dipole in an External Field |
82%
From NCERT
AIPMT - 2006
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Charges +q and –q are placed at points A and B, respectively; which are at a distance 2L apart. C is the midpoint between A and B. The work done in moving a charge +Q along the semicircle CRD is:

1. $\frac{qQ}{4{\mathrm{\pi \epsilon }}_{0}\mathrm{L}}$
2. $\frac{qQ}{2{\mathrm{\pi \epsilon }}_{0}\mathrm{L}}$
3. $\frac{qQ}{6{\mathrm{\pi \epsilon }}_{0}\mathrm{L}}$
4. $-\frac{qQ}{6{\mathrm{\pi \epsilon }}_{0}\mathrm{L}}$

Subtopic:  Electric Potential Energy |
59%
From NCERT
AIPMT - 2007
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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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The energy required to charge a parallel plate condenser of plate separation, $$d$$ and plate area of cross-section, $$A$$ such that the uniform electric field between the plates is $$E,$$ is:
1. $\frac{1}{2}$ ${\mathrm{\epsilon }}_{0}{\mathrm{E}}^{2}/\mathrm{Ad}$

2. ${\mathrm{\epsilon }}_{0}{\mathrm{E}}^{2}/\mathrm{Ad}$

3. ${\mathrm{\epsilon }}_{0}{\mathrm{E}}^{2}\mathrm{Ad}$

4. $\frac{1}{2}$ ${\mathrm{\epsilon }}_{0}{\mathrm{E}}^{2}\mathrm{Ad}$

Subtopic:  Capacitance |
From NCERT
AIPMT - 2008
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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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Three capacitors each of capacitance $$C$$ and of breakdown voltage $$V$$ are joined in series. The capacitance and breakdown voltage of the combination will be:
1. $\frac{C}{3},$ $\frac{V}{3}$

2. $3C,$ $\frac{V}{3}$

3. $\frac{C}{3},$ $3V$

4. $$3C,~3V$$

Subtopic:  Combination of Capacitors |
81%
From NCERT
AIPMT - 2009
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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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