# Four electric charges $$+ q,$$ $$+ q,$$ $$- q$$ and $$- q$$ are placed at the corners of a square of side $$2L$$ (see figure). The electric potential at point $$A$$, mid-way between the two charges $$+ q$$ and $$+ q$$ is:                1. $$\frac{1}{4 \pi\varepsilon_{0}} \frac{2 q}{L} \left(1 + \frac{1}{\sqrt{5}}\right)$$ 2. $$\frac{1}{4 \pi\varepsilon_{0}} \frac{2 q}{L} \left(1 - \frac{1}{\sqrt{5}}\right)$$ 3. zero 4. $$\frac{1}{4 \pi \varepsilon_{0}} \frac{2 q}{L} \left(1 + \sqrt{5}\right)$$

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 $$a,b, ~\text{and}~c$$ $$(a<b<c)$$ and have surface charge densities $$\sigma, -\sigma, ~\text{and}~\sigma$$ respectively. If $$V_A, V_B~\text{and}~V_C$$ 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 |
81%
From NCERT
AIPMT - 2009
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The electric potential at a point (x, y, z) is given by V = -x2y - xz3 + 4.
The electric field $\stackrel{\to }{E}$ at that point is:
1. $\stackrel{\to }{E}$= (2xy + z3)$\stackrel{^}{\mathrm{i}}$ + x2$\stackrel{^}{\mathrm{j}}$ + 3xz2$\stackrel{^}{\mathrm{k}}$
2. $\stackrel{\to }{E}$ = 2xy$\stackrel{^}{\mathrm{i}}$ + (x2 +y2)$\stackrel{^}{\mathrm{j}}$ +(3xz-y2)$\stackrel{^}{\mathrm{k}}$
3. $\stackrel{\to }{E}$ = z3$\stackrel{^}{\mathrm{i}}$ + xyz$\stackrel{^}{\mathrm{j}}$ + z2$\stackrel{^}{\mathrm{k}}$
4. $\stackrel{\to }{E}$ = (2xy- z3)$\stackrel{^}{\mathrm{i}}$ + xy2$\stackrel{^}{\mathrm{j}}$ + 3z2x$\stackrel{^}{\mathrm{k}}$
Subtopic:  Relation between Field & Potential |
79%
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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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. $$\dfrac{pE}{2}$$
3. $$2pE$$
4. $$pE$$

Subtopic:  Energy of Dipole in an External Field |
82%
From NCERT
AIPMT - 2006
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