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 |
 79%
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. 12 ε0E2/Ad

2. ε0E2/Ad

3. ε0E2Ad

4. 12 ε0E2Ad

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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An electric dipole of moment \(\vec {p} \) is lying along a uniform electric field \(\vec{E}\). The work done in rotating the dipole by \(90^{\circ}\) is:
1. \(\sqrt{2}pE\)
2. \(\dfrac{pE}{2}\)
3. \(2pE\)
4. \(pE\)

Subtopic:  Energy of Dipole in an External Field |
 82%
From NCERT
AIPMT - 2006
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