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. \(\dfrac{-q^2}{4\pi\varepsilon_0d}\Big(6-\dfrac{1}{\sqrt2}\Big)\)
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 2L apart. C is the midpoint between A and B. The work done in moving a charge +Q along the semicircle CRD is:
   
1. qQ4πε0L
2. qQ2πε0L
3. qQ6πε0L
4. -qQ6πε0L

Subtopic:  Electric Potential Energy |
 59%
From NCERT
AIPMT - 2007
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Two charges q1 and q2 are placed 30 cm apart, as shown in the figure. A third charge q3 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 q34π0k , where k is:

.

1. 8q2

2. 6q2

3. 8q1

4. 6q1

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. \(2U\)

Subtopic:  Electric Potential Energy |
 53%
From NCERT
AIPMT - 2000
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