# 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 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 $$+q$$ 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 is conducted to a battery as shown in the figure. The ratio of the charges on 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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