A parallel plate condenser has a uniform electric field \(E\) (V/m) in the space between the plates. If the distance between the plates is \(d\) (m) and the area of each plate is \(A\) (m2), the energy (joule) stored in the condenser is:
1. \( \frac{1}{2}\varepsilon_0{E}^2 \)
2. \( \frac{{E}^2 {Ad}}{\varepsilon_0} \)
3. \( \frac{1}{2}\varepsilon_0 E^2 Ad \)
4. \(\varepsilon_0 EAd \)

Subtopic:  Energy stored in Capacitor |
 90%
From NCERT
NEET - 2021
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Four electric charges \(+ q,\) \(+ q,\) \(- q\) and \(- q\) are placed at the corners of a square of side \(2L\) (see figure). The electric potential at point \(A\), mid-way between the two charges \(+ q\) and \(+ q\) is:
              
1. \(\frac{1}{4 \pi\varepsilon_{0}} \frac{2 q}{L} \left(1 + \frac{1}{\sqrt{5}}\right)\)
2. \(\frac{1}{4 \pi\varepsilon_{0}} \frac{2 q}{L} \left(1 - \frac{1}{\sqrt{5}}\right)\)
3. zero
4. \(\frac{1}{4 \pi \varepsilon_{0}} \frac{2 q}{L} \left(1 + \sqrt{5}\right)\)

Subtopic:  Electric Potential |
 73%
From NCERT
AIPMT - 2011
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A series combination of n1 capacitors, each of value C1, is charged by a source of potential difference 4V. When another parallel combination of n2 capacitors, each of value C2, is charged by a source of potential difference V, it has the same (total) energy stored in it, as the first combination has. The value of C2, in terms of C1, is then:

1. 2C1n1n2

2. 16n2n1C1

3. 2n2n1C1

4. 16C1n1n2

Subtopic:  Energy stored in Capacitor |
 73%
From NCERT
AIPMT - 2010
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Three concentric spherical shells have radii \(a,b, ~\text{and}~c\) \((a<b<c)\) and have surface charge densities \(\sigma, -\sigma, ~\text{and}~\sigma\) respectively. If \(V_A, V_B~\text{and}~V_C\) denote the potential of the three shells, and \(c= a+b\), it can be concluded that:
1. \(\mathrm{V}_{\mathrm{C}}=\mathrm{V}_{\mathrm{A}} \neq \mathrm{V}_{\mathrm{B}}\)
2. \(\mathrm{V}_{\mathrm{C}}=\mathrm{V}_B \neq \mathrm{V}_{\mathrm{A}}\)
3. \(\mathrm{V}_{\mathrm{C}} \neq \mathrm{V}_B \neq \mathrm{V}_A\)
4. \(\mathrm{V}_{\mathrm{C}}=\mathrm{V}_B=\mathrm{V}_A\)

Subtopic:  Electric Potential |
From NCERT
AIPMT - 2009
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Three capacitors each of capacitance \(C\) and of breakdown voltage \(V\) are joined in series. The capacitance and breakdown voltage of the combination will be:
1. C3, V3

2. 3C, V3

3. C3, 3V

4. \(3C,~3V\)

Subtopic:  Combination of Capacitors |
 81%
From NCERT
AIPMT - 2009
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The electric potential at a point (x, y, z) is given by V = -x2y - xz3 + 4.
The electric field E at that point is:
1. E= (2xy + z3)i^ + x2j^ + 3xz2k^
2. E = 2xyi^ + (x2 +y2)j^ +(3xz-y2)k^
3. E = z3i^ + xyzj^ + z2k^
4. E = (2xy- z3)i^ + xy2j^ + 3z2xk^
Subtopic:  Relation between Field & Potential |
 80%
AIPMT - 2009
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The electric potential at a point in free space due to a charge \(Q\) coulomb is \(Q\times10^{11}~\text{V}\). The electric field at that point is:
1. \(4\pi \varepsilon_0 Q\times 10^{22}~\text{V/m}\)
2. \(12\pi \varepsilon_0 Q\times 10^{20}~\text{V/m}\)
3. \(4\pi \varepsilon_0 Q\times 10^{20}~\text{V/m}\)
4. \(12\pi \varepsilon_0 Q\times 10^{22}~\text{V/m}\)

Subtopic:  Relation between Field & Potential |
 72%
From NCERT
AIPMT - 2008
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The energy required to charge a parallel plate condenser of plate separation, \(d\) and plate area of cross-section, \(A\) such that the uniform electric field between the plates is \(E,\) is:
1. \(\frac{\varepsilon_0E^2}{2Ad}\)
2. \(\frac{\varepsilon_0E^2}{Ad}\)
3. \(\varepsilon_0E^2Ad\)
4. \(\frac{1}{2}\varepsilon_0E^2Ad\)

Subtopic:  Capacitance |
From NCERT
AIPMT - 2008
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Two condensers, one of capacity \(C\) and the other of capacity \(\frac{C}2\) are connected to a \(V\) volt battery, as shown in the figure. 
           
The energy stored in the capacitors when both condensers are fully charged will be:
1. \(2CV^2\)
2. \({1 \over4}CV^2\)
3. \({3 \over4}CV^2\)
4. \({1 \over2}CV^2\)

Subtopic:  Energy stored in Capacitor |
 83%
From NCERT
AIPMT - 2007
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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. qQ4πε0L
2. qQ2πε0L
3. qQ6πε0L
4. -qQ6πε0L

Subtopic:  Electric Potential Energy |
 59%
From NCERT
AIPMT - 2007
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