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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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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 |

55%

From NCERT

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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 $\mathrm{V}=4v\mathrm{olt}$, each plate of the capacitor has a surface area of ${10}^{-2}{\mathrm{m}}^{2}$ and the plates are $0.1\times {10}^{-3}\mathrm{m}$ apart, then the number of excess electrons on the negative plate is:

1. $5.15\times {10}^{9}$

2. $2.21\times {10}^{10}$

3. $3.33\times {10}^{9}$

4. $2.21\times {10}^{9}$

Subtopic: Capacitance |

65%

From NCERT

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Two equal charges *q* of opposite sign separated by a distance 2*a* 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* >> 2*a*) (Where *p* = 2*qa*)

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 K_{1}&K_{2} (${K}_{1}<{K}_{2}$) 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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