If potential [in volts] in a region is expressed as V [x, y, z] = 6xy- y + 2yz, the electric field [in N/C] at point [1, 1, 0] is -
1. $-\left(3\stackrel{^}{\mathrm{i}}+5\stackrel{^}{\mathrm{j}}+3\stackrel{^}{\mathrm{k}}\right)$
2. $-\left(6\stackrel{^}{\mathrm{i}}+5\stackrel{^}{\mathrm{j}}+2\stackrel{^}{\mathrm{k}}\right)$
3. $-\left(2\stackrel{^}{\mathrm{i}}+3\stackrel{^}{\mathrm{j}}+\stackrel{^}{\mathrm{k}}\right)$
4. $-\left(6\stackrel{^}{\mathrm{i}}+9\stackrel{^}{\mathrm{j}}+\stackrel{^}{\mathrm{k}}\right)$
Subtopic:  Relation between Field & Potential |
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A parallel plate air capacitor has capacity 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. $\frac{{C}^{2}{V}^{2}}{2d}$

2. $\frac{C{V}^{2}}{2d}$

3. $\frac{C{V}^{2}}{d}$

4. $\frac{{C}^{2}{V}^{2}}{2{d}^{2}}$

Subtopic:  Combination of Capacitors |
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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 |
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Two thin dielectric slabs of dielectric constants Kand K2 (K< K2) 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 plate P is correctly shown by:

1.      2.
3.             4.
Subtopic:  Dielectrics in Capacitors |
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A conducting sphere of 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 $\frac{Q}{4{\mathrm{\pi \epsilon }}_{0}{\mathrm{R}}^{2}}$

2. $\frac{Q}{4{\mathrm{\pi \epsilon }}_{0}\mathrm{R}}$ and zero

3. $\frac{Q}{4{\mathrm{\pi \epsilon }}_{0}\mathrm{R}}$ and $\frac{Q}{4{\mathrm{\pi \epsilon }}_{0}{\mathrm{R}}^{2}}$

4. both are zero.

Subtopic:  Electric Potential |
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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 point (1, 1,1) is:
1. $$6\sqrt5$$ N
2. $$30$$ N
3. $$24$$ N
4. $$4\sqrt35$$ N

Subtopic:  Relation between Field & Potential |
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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 |
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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 $\theta =90°$, the torque and the potential energy of the dipole will respectively be:
1. $pE\mathrm{sin}\theta ,-pE\mathrm{cos}\theta$
2. $pE\mathrm{sin}\theta ,-2pE\mathrm{cos}\theta$
3.
4. $pE\mathrm{cos}\theta ,-pE\mathrm{sin}\theta$

Subtopic:  Energy of Dipole in an External Field |
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Four-point charges –Q, -q, 2q 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 |
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Two metallic spheres of radii 1 cm and 3cm are given charges of , respectively. If these are connected by a conducting wire , then the final charge on the bigger sphere is-

1.

2.

3.

4.

Subtopic:  Electric Potential |
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