# A conducting sphere of the radius $$R$$ is given a charge $$Q.$$ The electric potential and the electric field at the centre of the sphere respectively are: 1.  zero and $$\frac{Q}{4 \pi \varepsilon_0 {R}^2}$$ 2.  $$\frac{Q}{4 \pi \varepsilon_0 R}$$ and zero 3.  $$\frac{Q}{4 \pi \varepsilon_0 R}$$ and $$\frac{Q}{4 \pi \varepsilon_0{R}^2}$$ 4. both are zero

Subtopic:  Electric Potential |
83%
From NCERT
AIPMT - 2014
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In a region, the potential is represented by $$V=(x,y,z)=6x-8xy-8y+6yz,$$ where $$V$$ is in volts and $$x,y,z$$ are in meters. The electric force experienced by a charge of $$2$$ coulomb situated at a point $$(1,1,1)$$ is:
1. $$6\sqrt{5}~\text{N}$$
2. $$30~\text{N}$$
3. $$24~\text{N}$$
4. $$4\sqrt{35}~\text{N}$$

Subtopic:  Relation between Field & Potential |
73%
From NCERT
AIPMT - 2014
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$$A$$, $$B$$ and $$C$$ are three points in a uniform electric field. The electric potential is:

 1 maximum at $$B$$ 2 maximum at $$C$$ 3 same at all the three points $$A, B$$ and $$C$$ 4 maximum at $$A$$
Subtopic:  Relation between Field & Potential |
84%
From NCERT
AIPMT - 2013
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An electric dipole of moment $$p$$ is placed in an electric field of intensity $$E.$$ The dipole acquires a position such that the axis of the dipole makes an angle $$\theta$$ with the direction of the field. Assuming that the potential energy of the dipole to be zero when $$\theta = 90^{\circ}$$, the torque and the potential energy of the dipole will respectively be:
1. $$pE\text{sin}\theta, ~-pE\text{cos}\theta$$
2. $$pE\text{sin}\theta, ~-2pE\text{cos}\theta$$
3. $$pE\text{sin}\theta, ~2pE\text{cos}\theta$$
4. $$pE\text{cos}\theta, ~-pE\text{sin}\theta$$

Subtopic:  Energy of Dipole in an External Field |
81%
From NCERT
AIPMT - 2012
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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 |
90%
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 |
72%
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 |
81%
From NCERT
AIPMT - 2009
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