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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. | \(p E \sin \theta,-p E \cos \theta\) | 2. | \(p E \sin \theta,-2 p E \cos \theta\) |

3. | \(p E \sin \theta, 2 p E \cos \theta\) | 4. | \(p E \cos \theta,-p E \sin \theta\) |

Subtopic: Energy of Dipole in an External Field |

83%

From NCERT

NEET - 2012

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The equivalent capacitance of the following arrangement is:

1. \(18~\mu \text{F}\)

2. \(9~\mu \text{F}\)

3. \(6~\mu \text{F}\)

4. \(12~\mu \text{F}\)

Subtopic: Combination of Capacitors |

79%

From NCERT

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Two capacitors of capacitance \(6~\mu\text{F}\) and \(3~\mu\text{F}\) are connected in series with battery of \(30~\text{V}\). The charge on \(3~\mu\text{F}\) capacitor at a steady state is:

1. \( 3 ~\mu\text{C}\)

2. \( 1.5 ~\mu\text{C}\)

3. \( 60~\mu\text{C}\)

4. \( 900~\mu\text{C}\)

Subtopic: Combination of Capacitors |

85%

From NCERT

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Two concentric metallic spherical shells \(A\) and \(B\) of radii \(a\) and \(b\) respectively \((b>a)\) are arranged such that outer shell is earthed and inner shell is charged to \(Q\). Charge on the outer surface of outer shell will be:

1. \(- \frac{Q a}{b}\)

2. \(Q \left[1 - \frac{a}{b}\right]\)

3. \(-Q\)

4. zero

Subtopic: Electrostatic Shielding |

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The equivalent capacitance across \(A\) and \(B\) in the given figure is:

1. \( \frac{3}{2}\text{C}\)

2. \(\text{C}\)

3. \( \frac{2}{3}\text{C}\)

4. \( \frac{5}{3}\text{C}\)

Subtopic: Combination of Capacitors |

79%

From NCERT

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Two capacitors of capacity \(2~\mu\text{F}\) and \(3~\mu\text{F}\) are charged to the same potential difference of \(6\) V. Now they are connected with opposite polarity as shown. After closing switches \(S_1~\text{and}~S_2\), their final potential difference becomes:

1. | \(\text{zero} \) | 2. | \(\frac{4}{3}~\text{V} \) |

3. | \(3~\text{V} \) | 4. | \(\frac{6}{5}~\text{V} \) |

Subtopic: Combination of Capacitors |

63%

From NCERT

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Which of the following statements is correct regarding electrostatics of conductors?

1. | The interior of the conductor with no cavity can have no excess charge in the static situation. |

2. | Electrostatic potential is constant throughout the volume of the conductor. |

3. | Electrostatic potential has the same value inside as that on its surface. |

4. | All of these. |

Subtopic: Electrostatic Shielding |

88%

From NCERT

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A conducting sphere of radius \(R\) is given a charge \(Q\). The electric potential and field at the center of the sphere respectively are:

1. | Zero and \(\mathrm{Q} / 4 \pi \varepsilon_{\mathrm{o}} \mathrm{R}^2\) |

2. | \(\mathrm{Q} / 4 \pi \varepsilon_{\mathrm{O}} \mathrm{R}\) and zero |

3. | \(\mathrm{Q} / 4 \pi \varepsilon_{\mathrm{O}} \mathrm{R}\) and \(\mathrm{Q} / 4 \pi \varepsilon_{\mathrm{o}} \mathrm{R}^2\) |

4. | Both are zero |

Subtopic: Electrostatic Shielding |

86%

From NCERT

NEET - 2014

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Two thin dielectric slabs of dielectric constants \(K_1~\text{and}~K_2(K_{1} < K_{2})\) 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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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 \(\theta\) with the axis of the dipole, then the potential at \(P\) is given by: \((r>>2a)\) (Where \(p = 2qa\))

1. | \(V={p\cos \theta \over 4 \pi \varepsilon_0r^2}\) | 2. | \(V={p\cos \theta \over 4 \pi \varepsilon_0r}\) |

3. | \(V={p\sin \theta \over 4 \pi \varepsilon_0r}\) | 4. | \(V={p\cos \theta \over 2 \pi \varepsilon_0r^2}\) |

Subtopic: Electric Potential |

72%

From NCERT

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