# 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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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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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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The variation of potential with distance x from a fixed point is shown in the figure. The electric field at x =13 m is:

1. 7.5 volt/meter

2. –7.5 volt/meter

3. 5 volt/meter

4. –5 volt/meter

Subtopic:  Relation between Field & Potential |
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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The figure shows some of the equipotential surfaces. Magnitude and direction of the electric field is given by:

 1 200 V/m, making an angle $$120^\circ$$with the x-axis 2 100 V/m, pointing towards the negative x-axis 3 200 V/m, making an angle $$60^\circ$$with the x-axis 4 100 V/m, making an angle $$30^\circ$$with the x-axis

Subtopic:  Relation between Field & Potential |
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$$\mathrm{A}$$, $$\mathrm{B}$$ and $$\mathrm{C}$$ are three points in a uniform electric field. The electric potential is:

 1 maximum at $$\mathrm{A}$$ 2 maximum at $$\mathrm{B}$$ 3 maximum at $$\mathrm{C}$$ 4 same at all the three points $$\mathrm{A},\mathrm{B} ~\text{and}~\mathrm{C}$$
Subtopic:  Relation between Field & Potential |
82%
From NCERT
NEET - 2013
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In the given figure if , each plate of the capacitor has a surface area of  and the plates are  apart, then the number of excess electrons on the negative plate is:

1. $5.15×{10}^{9}$

2. $2.21×{10}^{10}$

3. $3.33×{10}^{9}$

4. $2.21×{10}^{9}$

Subtopic:  Capacitance |
65%
From NCERT
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Two equal charges q of opposite sign separated by a distance 2a constitute an electric dipole of dipole moment p. If P is a point at a distance r from the centre of the dipole and the line joining the centre of the dipole to this point makes an angle θ with the axis of the dipole, then the potential at P is given by: (r >> 2a) (Where p = 2qa

 1 $$V={pcos \theta \over 4 \pi \varepsilon_0r^2}$$ 2 $$V={pcos \theta \over 4 \pi \varepsilon_0r}$$ 3 $$V={psin \theta \over 4 \pi \varepsilon_0r}$$ 4 $$V={pcos \theta \over 2 \pi \varepsilon_0r^2}$$
Subtopic:  Electric Potential |
72%
From NCERT
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Two thin dielectric slabs of dielectric constants K1&K2 (${K}_{1}<{K}_{2}$) are inserted between plates of a parallel capacitor, as shown in the figure. The variation of electric field E between the plates with distance d as measured from plate P is correctly shown by:

 1 2 3 4
Subtopic:  Dielectrics in Capacitors |
77%
From NCERT
NEET - 2014
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