# The capacitance of a parallel plate capacitor with air as a medium is $$6~\mu\text{F}$$. With the introduction of a dielectric medium, the capacitance becomes $$30~\mu\text{F}$$. The permittivity of the medium is:$$\left(\varepsilon_0=8.85 \times 10^{-12} ~\text{C}^2 \text{N}^{-1} \text{m}^{-2}\right )$$ 1. $$1.77 \times 10^{-12}~ \text{C}^2 \text{N}^{-1} \text{m}^{-2}$$ 2. $$0.44 \times 10^{-10} ~\text{C}^2 \text{N}^{-1} \text{m}^{-2}$$ 3. $$5.00 ~\text{C}^2 \text{N}^{-1} \text{m}^{-2}$$ 4. $$0.44 \times 10^{-13} ~\text{C}^2 \text{N}^{-1} \text{m}^{-2}$$

Subtopic:  Dielectrics in Capacitors |
61%
From NCERT
NEET - 2020
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A short electric dipole has a dipole moment of $$16 \times 10^{-9} ~\text{C-}\text{m}$$. The electric potential due to the dipole at a point at a distance of $$0.6~\text{m}$$ from the centre of the dipole situated on a line making an angle of $$60^{\circ}$$ with the dipole axis is: $$\left( \frac{1}{4\pi \varepsilon_0}= 9\times 10^{9}~\text{N-m}^2/\text{C}^2\right)$$
1. $$200~\text{V}$$
2. $$400~\text{V}$$
3. zero
4. $$50~\text{V}$$

Subtopic:  Energy of Dipole in an External Field |
66%
From NCERT
NEET - 2020
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In a certain region of space with volume $$0.2$$ m3, the electric potential is found to be $$5$$ V throughout. The magnitude of electric field in this region is:
1. $$0.5$$ N/C
2. $$1$$ N/C
3. $$5$$ N/C
4. zero

Subtopic:  Relation between Field & Potential |
75%
From NCERT
NEET - 2020
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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 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 identical capacitors $$C_{1}$$ and $$C_{2}$$ of equal capacitance are connected as shown in the circuit. Terminals $$a$$ and $$b$$ of the key $$k$$ are connected to charge capacitor $$C_{1}$$ using a battery of emf $$V$$ volt. Now disconnecting $$a$$ and $$b$$ terminals, terminals $$b$$ and $$c$$ are connected. Due to this, what will be the percentage loss of energy?

1. $$75\%$$
2. $$0\%$$
3. $$50\%$$
4. $$25\%$$

Subtopic:  Energy stored in Capacitor |
63%
From NCERT
NEET - 2019
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Two metal spheres, one of radius $$R$$ and the other of radius $$2R$$ respectively have the same surface charge density $$\sigma.$$ They are brought in contact and separated.  What will be the new surface charge densities on them?
1. $$\sigma_{1}=\frac{5}{6}\sigma ,~\sigma_{2}=\frac{5}{6}\sigma$$
2. $$\sigma_{1}=\frac{5}{2}\sigma ,~\sigma_{2}=\frac{5}{6}\sigma$$
3. $$\sigma_{1}=\frac{5}{2}\sigma ,~\sigma_{2}=\frac{5}{3}\sigma$$
4. $$\sigma_{1}=\frac{5}{3}\sigma ,~\sigma_{2}=\frac{5}{6}\sigma$$
Subtopic:  Electric Potential |
55%
From NCERT
NEET - 2019
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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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