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An elementary particle of mass *m* and charge +*e* is projected with velocity *v* at a much more massive particle of charge *Ze*, where *Z* > 0. What is the closest possible approach of the incident particle?

1. | \(\frac{Z e^2}{2 \pi \varepsilon_0 m v^2} \) | 2. | \(\frac{Z_e}{4 \pi \varepsilon_0 m v^2} \) |

3. | \(\frac{Z e^2}{8 \pi \varepsilon_0 m v^2} \) | 4. | \(\frac{Z_e}{8 \pi \varepsilon_0 m v^2}\) |

Subtopic: Electric Potential Energy |

65%

From NCERT

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A parallel plate capacitor of capacitance *C* is connected to a battery and is charged to a potential difference *V*. Another capacitor of capacitance 2*C* is connected to another battery and is charged to potential difference 2*V*. The charging batteries are now disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is?

1. Zero

2. $\frac{25C{V}^{2}}{6}$

3. $\frac{3C{V}^{2}}{2}$

4. $\frac{9C{V}^{2}}{2}$

Subtopic: Energy stored in Capacitor |

53%

From NCERT

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Consider two points 1 and 2 in a region outside a charged sphere. Two points are not very far away from the sphere. If *E* and *V* represent the electric field vector and the electric potential, which of the following is not possible?

1. | \(\left|\vec{E}_1\right|=\left|\vec{E}_2\right|, V_1=V_2\) |

2. | \(\vec{E}_1 \neq \vec{E}_2, V_1 \neq V_2\) |

3. | \(\vec{E}_1 \neq \vec{E}_2, V_1=V_2\) |

4. | \(\left|\vec{E}_1\right|=\left|\vec{E}_2\right|, V_1 \neq V_2\) |

Subtopic: Relation between Field & Potential |

From NCERT

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A parallel plate capacitor has capacitance *\(C\)*. If it is equally filled with parallel layers of materials of dielectric constants \(K_1\) and \(K_2\), its capacity becomes \(C_1\). The ratio of \(C_1\) to *\(C\)* is:

1. | \(K_1 + K_2\) | 2. | \(\frac{K_{1} K_{2}}{K_{1}-K_{2}}\) |

3. | \(\frac{K_{1}+K_{2}}{K_{1} K_{2}}\) | 4. | \(\frac{2 K_{1} K_{2}}{K_{1}+K_{2}}\) |

Subtopic: Dielectrics in Capacitors |

69%

From NCERT

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The equivalent capacitance between *A* and *B* is:

1. | 2 μF |
2. | 3 μF |

3. | 5 μF |
4. | 0.5 μF |

Subtopic: Combination of Capacitors |

71%

From NCERT

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100 capacitors each having a capacity of 10 μ*F* are connected in parallel and are charged by a potential difference of 100 *kV*. The energy stored in the capacitors and the cost of charging them, if electrical energy costs 108 paise per *kWh*, will be?

1. | 10^{7} joule and 300 paise |

2. | 5 × 10^{6} joule and 300 paise |

3. | 5 × 10^{6} joule and 150 paise |

4. | 10^{7} joule and 150 paise |

Subtopic: Energy stored in Capacitor |

56%

From NCERT

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A series combination of n_{1} capacitors, each of value C_{1}, is charged by a source of potential difference 4 V. When another parallel combination of n_{2} capacitors, each of value C_{2}, 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 C_{2} in terms of C_{1} is:

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 |

71%

From NCERT

NEET - 2010

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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 area of each plate is $\mathrm{A}\left({\mathrm{m}}^{2}\right)$, the energy (joule) stored in the condenser is:

1. $\frac{1}{2}{\mathrm{\epsilon}}_{0}{\mathrm{E}}^{2}$

2. ${\mathrm{\epsilon}}_{0}\mathrm{EAd}$

3. $\frac{1}{2}{\mathrm{\epsilon}}_{0}{\mathrm{E}}^{2}\mathrm{Ad}$

4. ${\mathrm{E}}^{2}\mathrm{Ad}/{\mathrm{\epsilon}}_{0}$

Subtopic: Energy stored in Capacitor |

80%

From NCERT

NEET - 2021

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Two metallic spheres of radii 1 cm and 3 cm are given charges of -1$\times {10}^{-2}\mathrm{C}$ and $5\times {10}^{-2}\mathrm{C}$, respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is:

1. $2\times {10}^{-2}\mathrm{C}$

2. $3\times {10}^{-2}\mathrm{C}$

3. $4\times {10}^{-2}\mathrm{C}$

4. $1\times {10}^{-2}\mathrm{C}$

Subtopic: Electric Potential |

68%

From NCERT

NEET - 2012

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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 |

83%

From NCERT

NEET - 2013

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