In a region, the potential is represented by \(V=(x,y,z)=6x-8xy-8y+6yz,\) where \(V\) is in volts and \(x,y,z\) are in meters. The electric force experienced by a charge of \(2\) coulomb situated at a point \((1,1,1)\) is:
1. \(6\sqrt{5}~\text{N}\)
2. \(30~\text{N}\)
3. \(24~\text{N}\)
4. \(4\sqrt{35}~\text{N}\)

Subtopic:  Relation between Field & Potential |
 74%
From NCERT
AIPMT - 2014
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\(A\), \(B\) and \(C\) are three points in a uniform electric field. The electric potential is: 

     
1. maximum at \(B\)
2. maximum at \(C\)
3. same at all the three points \(A, B\) and \(C\)
4. maximum at \(A\)
Subtopic:  Relation between Field & Potential |
 84%
From NCERT
AIPMT - 2013
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An electric dipole of moment \(p\) is placed in an electric field of intensity \(E.\) The dipole acquires a position such that the axis of the dipole makes an angle \(\theta\) with the direction of the field. Assuming that the potential energy of the dipole to be zero when \(\theta = 90^{\circ}\), the torque and the potential energy of the dipole will respectively be:
1. \(pE\text{sin}\theta, ~-pE\text{cos}\theta\)
2. \(pE\text{sin}\theta, ~-2pE\text{cos}\theta\)
3. \(pE\text{sin}\theta, ~2pE\text{cos}\theta\)
4. \(pE\text{cos}\theta, ~-pE\text{sin}\theta\)

Subtopic:  Energy of Dipole in an External Field |
 81%
From NCERT
AIPMT - 2012
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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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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 |
 84%
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. \(\frac{pE}{2}\)
3. \(2pE\)
4. \(pE\)

Subtopic:  Energy of Dipole in an External Field |
 82%
From NCERT
AIPMT - 2006
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A parallel plate air capacitor is charged to a potential difference of V volts. After disconnecting the charging battery, the distance between the plates of the capacitor is increased using an insulating handle. As a result the potential difference between the plates:

1. decreases.

2. does not change.

3. becomes zero.

4. increases.

Subtopic:  Capacitance |
 56%
From NCERT
AIPMT - 2006
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