# 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. $$Q= 2q$$

Subtopic:  Electric Potential |
75%
From NCERT
AIPMT - 2012
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A parallel plate condenser has a uniform electric field $$E$$ (V/m) in the space between the plates. If the distance between the plates is $$d$$ (m) and the area of each plate is $$A$$ (m2), the energy (joule) stored in the condenser is:
1. $$\frac{1}{2}\varepsilon_0{E}^2$$
2. $$\frac{{E}^2 {Ad}}{\varepsilon_0}$$
3. $$\frac{1}{2}\varepsilon_0 E^2 Ad$$
4. $$\varepsilon_0 EAd$$

Subtopic:  Energy stored in Capacitor |
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From NCERT
NEET - 2021
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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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A series combination of n1 capacitors, each of value C1, is charged by a source of potential difference 4V. When another parallel combination of n2 capacitors, each of value C2, is charged by a source of potential difference V, it has the same (total) energy stored in it, as the first combination has. The value of C2, in terms of C1, is then:

1. $\frac{2{C}_{1}}{{n}_{1}{n}_{2}}$

2. $16\frac{{n}_{2}}{{n}_{1}}{C}_{1}$

3. $2\frac{{n}_{2}}{{n}_{1}}{C}_{1}$

4. $\frac{16{C}_{1}}{{n}_{1}{n}_{2}}$

Subtopic:  Energy stored in Capacitor |
73%
From NCERT
AIPMT - 2010
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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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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 |
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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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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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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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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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