# A parallel plate capacitor with cross-sectional area $$A$$ and separation $$d$$ has air between the plates. An insulating slab of the same area but the thickness of $$\frac{d}{2}$$ is inserted between the plates as shown in the figure having a dielectric constant, $$K=4$$. The ratio of new capacitance to its original capacitance will be:       1. $$2:1$$ 2. $$8:5$$ 3. $$6:5$$ 4. $$4:1$$

Subtopic:  Dielectrics in Capacitors |
74%
From NCERT
NEET - 2020
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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 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 |
82%
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 = volt. The electric field at the point (1, 0, 2) in volt/meter, is:

 1 8 along the negative X-axis 2 8 along the positive X-axis 3 16 along the negative X-axis 4 16 along the positive X-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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The variation of electrostatic potential with radial distance $$r$$ from the centre of a positively charged metallic thin shell of radius $$R$$ is given by the graph:

 1 2 3 4
Subtopic:  Electric Potential |
71%
From NCERT
NEET - 2020
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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. U/2

2. U/4

3. 4 U

4. 2 U

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 $$\mathrm{+q}$$ 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 $$\left(\frac{-\mathrm{qQ}}{4 \pi \varepsilon_0} \frac{1}{\mathrm{a}^2}\right) \sqrt{2} \mathrm{a}$$ 2 zero 3 $$\left(\frac{\mathrm{qQ}}{4 \pi \varepsilon_0} \frac{1}{\mathrm{a}^2}\right) \frac{1}{\sqrt{2}}$$ 4 $$\left(\frac{\mathrm{qQ}}{4 \pi \varepsilon_0} \frac{1}{\mathrm{a}^2}\right) \sqrt{2} \mathrm{a}$$
Subtopic:  Electric Potential Energy |
85%
From NCERT
AIPMT - 2005
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