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. $-\left(3\hat{\mathrm{i}}+5\hat{\mathrm{j}}+3\hat{\mathrm{k}}\right)$

2. $-\left(6\hat{\mathrm{i}}+5\hat{\mathrm{j}}+2\hat{\mathrm{k}}\right)$

3. $-\left(2\hat{\mathrm{i}}+3\hat{\mathrm{j}}+\hat{\mathrm{k}}\right)$

4. $-\left(6\hat{\mathrm{i}}+9\hat{\mathrm{j}}+\hat{\mathrm{k}}\right)$

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 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 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

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 $\theta =90\xb0$, 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. $pE\mathrm{sin}\theta ,2pE\mathrm{cos}\theta $

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 $-1\times {10}^{-2}Cand5\times {10}^{-2}C$, respectively. If these are connected by a conducting wire , then the final charge on the bigger sphere is-

1. $3\times {10}^{-2}C$

2. $4\times {10}^{-2}C$

3. $1\times {10}^{-2}C$

4. $2\times {10}^{-2}C$

Subtopic: Electric Potential |

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