When a particle with charge \(+q\) is thrown with an initial velocity \(v\) towards another stationary change \(+Q,\) it is repelled back after reaching the nearest distance \(r\) from \(+Q.\) The closest distance that it can reach if it is thrown with an initial velocity \(2v,\) is:

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

3. | \(\dfrac{r}{16}\) | 4. | \(\dfrac{r}{8}\) |

Subtopic: Electric Potential Energy |

68%

From NCERT

NEET - 2022

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Six charges \(+q,\) \(-q,\) \(+q,\) \(-q,\) \(+q\) and \(-q\) are fixed at the corners of a hexagon of side \(d\) as shown in the figure. The work done in bringing a charge \(q_0\) to the centre of the hexagon from infinity is:

(\(\varepsilon_0-\)permittivity of free space)

1. zero

2. \(\dfrac{-q^2}{4\pi\varepsilon_0d}\)

3. \(\dfrac{-q^2}{4\pi\varepsilon_0d}\Big(3-\dfrac{1}{\sqrt2}\Big)\)

4. \(\dfrac{-q^2}{4\pi\varepsilon_0d}\Big(6-\dfrac{1}{\sqrt2}\Big)\)

(\(\varepsilon_0-\)permittivity of free space)

1. zero

2. \(\dfrac{-q^2}{4\pi\varepsilon_0d}\)

3. \(\dfrac{-q^2}{4\pi\varepsilon_0d}\Big(3-\dfrac{1}{\sqrt2}\Big)\)

4. \(\dfrac{-q^2}{4\pi\varepsilon_0d}\Big(6-\dfrac{1}{\sqrt2}\Big)\)

Subtopic: Electric Potential Energy |

82%

From NCERT

NEET - 2022

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Charges +*q* and –*q* are placed at points *A* and *B,* respectively; which are at a distance 2*L* apart. *C* is the midpoint between *A* and *B*. The work done in moving a charge +Q along the semicircle *CRD* is:

1. $\frac{qQ}{4{\mathrm{\pi \epsilon}}_{0}\mathrm{L}}$

2. $\frac{qQ}{2{\mathrm{\pi \epsilon}}_{0}\mathrm{L}}$

3. $\frac{qQ}{6{\mathrm{\pi \epsilon}}_{0}\mathrm{L}}$

4. $-\frac{qQ}{6{\mathrm{\pi \epsilon}}_{0}\mathrm{L}}$

Subtopic: Electric Potential Energy |

59%

From NCERT

AIPMT - 2007

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

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

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

Subtopic: Electric Potential Energy |

85%

From NCERT

AIPMT - 2005

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If identical charges \((-q)\) are placed at each corner of a cube of side \(b\) then the electrical potential energy of charge \((+q)\) which is placed at centre of the cube will be:

1. \(\frac{- 4 \sqrt{2} q^{2}}{\pi\varepsilon_{0} b}\)

2. \(\frac{- 8 \sqrt{2} q^{2}}{\pi\varepsilon_{0} b}\)

3. \(\frac{- 4 q^{2}}{\sqrt{3} \pi\varepsilon_{0} b}\)

4. \(\frac{8 \sqrt{2} q^{2}}{4 \pi\varepsilon_{0} b}\)

Subtopic: Electric Potential Energy |

63%

From NCERT

AIPMT - 2002

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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. \(\frac{U}{2}\)

2. \(\frac{U}{4}\)

3. \(4U\)

4. \(2U\)

1. \(\frac{U}{2}\)

2. \(\frac{U}{4}\)

3. \(4U\)

4. \(2U\)

Subtopic: Electric Potential Energy |

53%

From NCERT

AIPMT - 2000

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