If potential $$[\text{in volts}]$$ in a region is expressed as $$V[x,y,z] = 6xy-y+2yz,$$ the electric field $$[\text{in N/C}]$$ at point $$(1, 1, 0)$$ is:

 1 $$- \left(3 \hat{i} + 5 \hat{j} + 3 \hat{k}\right)$$ 2 $$- \left(6 \hat{i} + 5 \hat{j} + 2 \hat{k}\right)$$ 3 $$- \left(2 \hat{i} + 3 \hat{j} + \hat{k}\right)$$ 4 $$- \left(6 \hat{i} + 9 \hat{j} + \hat{k}\right)$$
Subtopic:  Relation between Field & Potential |
84%
From NCERT
NEET - 2015
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A parallel plate air capacitor has capacitance $$C,$$ the distance of separation between plates is $$d$$ and potential difference $$V$$ is applied between the plates. The force of attraction between the plates of the parallel plate air capacitor is:

 1 $$\frac{C^2V^2}{2d}$$ 2 $$\frac{CV^2}{2d}$$ 3 $$\frac{CV^2}{d}$$ 4 $$\frac{C^2V^2}{2d^2}$$
Subtopic:  Capacitance |
69%
From NCERT
NEET - 2015
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A parallel plate air capacitor of capacitance $$C$$ is connected to a cell of emf $$V$$ and then disconnected from it. A dielectric slab of dielectric constant $$K,$$ which can just fill the air gap of the capacitor is now inserted in it. Which of the following is incorrect?

 1 the potential difference between the plates decreases $$K$$ times. 2 the energy stored in the capacitor decreases $$K$$ times. 3 the change in energy stored is $$\frac{1}{2}CV^{2}\left ( \frac{1}{K} -1\right )$$ 4 the charge on the capacitor is not conserved.

Subtopic:  Energy stored in Capacitor |
71%
From NCERT
NEET - 2015
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Two thin dielectric slabs of dielectric constants $$K_1$$ and $$K_2$$ $$(K_1<K_2)$$ are inserted between plates of a parallel plate capacitor, as shown in the figure. The variation of electric field $$'E'$$ between the plates with distance $$'d'$$ as measured from the plate $$P$$ is correctly shown by:

 1 2 3 4
Subtopic:  Dielectrics in Capacitors |
77%
From NCERT
AIPMT - 2014
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A conducting sphere of the radius $$R$$ is given a charge $$Q.$$ The electric potential and the electric field at the centre of the sphere respectively are:

 1 zero and $$\frac{Q}{4 \pi \varepsilon_0 {R}^2}$$ 2 $$\frac{Q}{4 \pi \varepsilon_0 R}$$ and zero 3 $$\frac{Q}{4 \pi \varepsilon_0 R}$$ and $$\frac{Q}{4 \pi \varepsilon_0{R}^2}$$ 4 both are zero
Subtopic:  Electric Potential |
83%
From NCERT
AIPMT - 2014
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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 |
73%
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 |
82%
From NCERT
AIPMT - 2012
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Four-point charges $$-Q, -q, 2q~\text{and}~2Q$$ are placed, one at each corner of the square. The relation between $$Q$$ and $$q$$ for which the potential at the center of the square is zero is:

 1 $$Q= -q$$ 2 $$Q= -2q$$ 3 $$Q= q$$ 4 $$Q= 2q$$
Subtopic:  Electric Potential |
76%
From NCERT
AIPMT - 2012
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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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