Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The potential \((V)\) at any axial point, at \(2~\text m\)  distance (\(r\)) from the centre of the dipole of dipole moment vector \(\vec P\) of magnitude, \(4\times10^{-6}~\text{C m},\) is \(\pm9\times10^3~\text{V}.\) (Take \({\dfrac{1}{4\pi\varepsilon_0}}=9\times10^9\) SI units)
Reason (R): \(V=\pm{\dfrac{2P}{4\pi\varepsilon_0r^2}},\) where \(r\) is the distance of any axial point situated at \(2~\text m\) from the centre of the dipole.
In the light of the above statements, choose the correct answer from the options given below:
1. Both (A) and (R) are True and (R) is not the correct explanation of (A).
2. (A) is True but (R) is False.
3. (A) is False but (R) is True.
4. Both (A) and (R) are True and (R) is the correct explanation of (A).
Subtopic:  Electric Potential |
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In the following circuit, the equivalent capacitance between terminal \(A\) and terminal \(B\) is:
                   
1. \(1~\mu\text F\)
2. \(0.5~\mu\text F\)
3. \(4~\mu\text F\)
4. \(2~\mu\text F\)
Subtopic:  Combination of Capacitors |
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A thin spherical shell is charged by some source. The potential difference between the two points \(C\) and \(P\) (in V) shown in the figure is: 
( Take \(\dfrac{1}{4 \pi \epsilon_0}=9 \times 10^9\) SI units)

1. \(1 \times 10^5\)
2. \(0.5 \times 10^5\)
3. \(\text{zero}\) 
4. \(3 \times 10^5\)
Subtopic:  Electric Potential |
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If the plates of a parallel plate capacitor connected to a battery are moved close to each other, then:
\(\mathrm A.\) the charge stored in it, increases.
\(\mathrm B.\) the energy stored in it, decreases.
\(\mathrm C.\) its capacitance increases.
\(\mathrm D.\) the ratio of charge to its potential remains the same.
\(\mathrm E.\) the product of charge and voltage increases.
 
Choose the most appropriate answer from the options given below:
1. \(\mathrm {A,C}\) and \(\mathrm E\) only
2. \(\mathrm {B,D }\) and \(\mathrm E\) only
3. \(\mathrm{A,B}\) and \(\mathrm C\) only
4. \(\mathrm{A,B}\) and \(\mathrm E\) only
Subtopic:  Energy stored in Capacitor |
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A dielectric slab of dielectric constant \(3\) having the same area of cross-section as that of parallel plate capacitor but of thickness \({\dfrac{3}{4}}^{\text{th}}\) of the separation of the plates is inserted into the capacitor. The ratio of potential difference across the plates without dielectric to that with dielectric is:
1. \(1:2\)
2. \(2:3\)
3. \(3:2\)
4. \(2:1\)
Subtopic:  Dielectrics in Capacitors |
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A \(12~\text{pF}\) capacitor is connected to a \(50~\text V\) battery, and the electrostatic energy stored in the capacitor in \(\text{nJ}\) is:
1. \(15\)
2. \(7.5\)
3. \(0.3\)
4. \(150\)
Subtopic:  Energy stored in Capacitor |
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The capacitance of a capacitor with charge \(q\) and a potential difference \(V\) depends on:
1. both \(q\)  and \(V\)
2. the geometry of the capacitor
3. \(q\) only
4. \(V\) only
Subtopic:  Capacitance |
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The value of the electric potential at a distance of \(9~\text{cm}\) from the point charge \(4\times10^{-7}~\text{C}\) is:
\(\left[\mathrm{Given}\dfrac{1}{4\pi\varepsilon_{0}}=9\times10^{9}~\text{N m}^{2}~\text{C}^{-2}\right]\)
1. \(4\times10^2~\text V\) 2. \(44.4~\text V\)
3. \(4.4\times10^5~\text V\) 4. \(4\times10^4~\text V\)
Subtopic:  Electric Potential |
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The equivalent capacitance of the system shown in the following circuit is:
1. \(9~{\mu \text{F}}\) 2. \(2~{\mu \text{F}}\)
3. \(3~{\mu \text{F}}\) 4. \(6~{\mu \text{F}}\)
Subtopic:  Combination of Capacitors |
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An electric dipole is placed as shown in the figure.

The electric potential (in \(10^2~\text{V}\)) at the point \(P\) due to the dipole is:
(\(\varepsilon_0=\) permittivity of free space and \(\dfrac{1}{4 \pi \varepsilon_0}=k\))
1. \(\left(\dfrac{8}{3}\right)qk\) 2. \(\left(\dfrac{3}{8}\right)qk\)
3. \(\left(\dfrac{5}{8}\right)qk\) 4. \(\left(\dfrac{8}{5}\right)qk\)
Subtopic:  Energy of Dipole in an External Field |
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