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A parallel plate capacitor has a uniform electric field \(E\) in the space between the plates. If the distance between the plates is \(d\) and the area of each plate is \(A,\) the energy stored in the capacitor is:

1. \(\frac{E^2 Ad}{\varepsilon_0}\)

2. \(\frac{1}{2}\varepsilon_0E^2 Ad\)

3. \(\varepsilon_0EAd\)

4. \(\frac{1}{2}\varepsilon_0E^2 \)

Subtopic: Energy stored in Capacitor |

92%

From NCERT

AIPMT - 2012

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Three charges, each \(+q\), are placed at the corners of an equilateral triangle \(ABC\) of sides \(BC\), \(AC\), and \(AB\). \(D\) and \(E\) are the mid-points of \(BC\) and \(CA\). The work done in taking a charge \(Q\) from \(D\) to \(E\) is:

1. | \(\frac{3qQ}{4\pi \varepsilon_0 a}\) | 2. | \(\frac{3qQ}{8\pi \varepsilon_0 a}\) |

3. | \(\frac{qQ}{4\pi \varepsilon_0 a}\) | 4. | \(\text{zero}\) |

Subtopic: Electric Potential |

83%

From NCERT

AIPMT - 2011

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The electric potential \(V\) at any point \((x,y,z)\), all in meters in space is given by \(V= 4x^2~\text{volt}\). The electric field at the point \((1,0,2)\) in volt/meter, is:

1. | \(8\) along the negative \(X\text-\)axis |

2. | \(8\) along the positive \(X\text-\)axis |

3. | \(16\) along the negative \(X\text-\)axis |

4. | \(16\) along the positive \(X\text-\)axis |

Subtopic: Relation between Field & Potential |

77%

From NCERT

AIPMT - 2011

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Two parallel metal plates having charges \(+Q\) and \(-Q\), face each other at a certain distance between them. If the plates are now dipped in the kerosene oil tank, the electric field between the plates will:

1. | increase. | 2. | decrease. |

3. | remain the same. | 4. | become zero. |

Subtopic: Dielectrics in Capacitors |

77%

From NCERT

AIPMT - 2010

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

1. \(3\times 10^{-2}~ \text{C}\)

2. \(4\times 10^{-2}~\text{C}\)

3. \(1\times 10^{-2}~\text{C}\)

4. \(2\times 10^{-2}~\text{C}\)

Subtopic: Electric Potential |

65%

From NCERT

AIPMT - 2012

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A capacitor is charged with a battery and energy stored is \(U.\) After disconnecting the battery another capacitor of the same capacity is connected in parallel with it. The energy stored in each capacitor is:

1. | \(\dfrac{U}{2}\) | 2. | \(\dfrac{U}{4}\) |

3. | \(4U\) | 4. | \(2U\) |

Subtopic: Electric Potential Energy |

53%

From NCERT

AIPMT - 2000

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Two charges q_{1} and q_{2} are placed 30 cm apart, as shown in the figure. A third charge q_{3} is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is $\frac{{\mathrm{q}}_{3}}{4\mathrm{\pi}{\in}_{0}}\mathrm{k}$ , where k is:

.

1. 8q_{2}

2. 6q_{2}

3. 8q_{1 }

4. 6q_{1}

Subtopic: Electric Potential Energy |

65%

From NCERT

AIPMT - 2005

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As per this diagram, a point charge \(+q\) is placed at the origin \(O.\) Work done in taking another point charge \(-Q\) from the point \(A,\) coordinates \((0,a),\) to another point \(B,\) coordinates \((a,0),\) along the straight path \(AB\) is:

1. | \( \left(\dfrac{-{qQ}}{4 \pi \varepsilon_0} \dfrac{1}{{a}^2}\right) \sqrt{2} {a}\) | 2. | zero |

3. | \( \left(\dfrac{qQ}{4 \pi \varepsilon_0} \dfrac{1}{{a}^2}\right) \dfrac{1}{\sqrt{2}} \) | 4. | \( \left(\dfrac{{qQ}}{4 \pi \varepsilon_0} \dfrac{1}{{a}^2}\right) \sqrt{2} {a}\) |

Subtopic: Electric Potential Energy |

85%

From NCERT

AIPMT - 2005

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A network of four capacitors of capacity equal to ${\mathrm{C}}_{1}=\mathrm{C},{\mathrm{C}}_{2}=2\mathrm{C},{\mathrm{C}}_{3}=3\mathrm{C}\text{, and}{\mathrm{C}}_{4}=4\mathrm{C}$ is conducted to a battery as shown in the figure. The ratio of the charges on ${\mathrm{C}}_{2}\text{and}{\mathrm{C}}_{4}$ is:

1. $\frac{7}{4}$

2. $\frac{22}{3}$

3. $\frac{3}{22}$

4. $\frac{4}{7}$

Subtopic: Combination of Capacitors |

71%

From NCERT

AIPMT - 2005

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The effective capacity of the network between terminals \(\mathrm{A}\) and \(\mathrm{B}\) is:

1. | \(6~\mu\text{F}~\) | 2. | \(20~\mu\text{F} ~\) |

3. | \(3~\mu\text{F}~\) | 4. | \(10~\mu\text{F}\) |

Subtopic: Combination of Capacitors |

90%

From NCERT

AIPMT - 1999

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