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. $\frac{qQ}{4{\mathrm{\pi \epsilon }}_{0}\mathrm{L}}$
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 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 $\frac{{\mathrm{q}}_{3}}{4\mathrm{\pi }{\in }_{0}}\mathrm{k}$ , 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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