The electric field in a certain region is acting radially outward and is given by E = Ar. A charge contained in a sphere of radius 'a' centered at the origin of the field will be given by:

1. \(4 \pi \varepsilon_{\mathrm{o}} \mathrm{A} \mathrm{a}^2\)

2. \(\varepsilon_{\mathrm{o}} \mathrm{A} \mathrm{a}^2\)

3. \(4 \pi \varepsilon_{\mathrm{o}} \mathrm{A} \mathrm{a}^3\)

4. \(\varepsilon_{\mathrm{o}} \mathrm{A} \mathrm{a}^3\)

Subtopic: Gauss's Law |

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Two pith balls carrying equal charges are suspended from a common point by strings of equal length, the equilibrium separation between them is r (as shown in Fig. I). Now, as shown in Fig. II, the strings are rigidly clamped at half the height. The equilibrium separation between the balls now becomes:

1. \(\frac{r}{\sqrt[3]{2}}\)

2. \(\frac{r}{\sqrt[2]{2}}\)

3. \(\frac{2r}{3}\)

4. none of the above

Subtopic: Coulomb's Law |

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What is the flux through a cube of side a, if a point charge of q is placed at one of its corners?

1. $\frac{2q}{{\epsilon}_{o}}$

2. $\frac{q}{8{\epsilon}_{o}}$

3. $\frac{q}{{\epsilon}_{o}}$

4. $\frac{q}{2{\epsilon}_{o}}$

Subtopic: Gauss's Law |

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A charge Q is enclosed by a Gaussian spherical surface of radius R. If the radius is doubled, then the outward electric flux will

1. be reduced to half

2. remain the same

3. be doubled

4. increase four times

1. be reduced to half

2. remain the same

3. be doubled

4. increase four times

Subtopic: Gauss's Law |

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Two positive ions, each carrying a charge q, are separated by a distance d. If F is the force of repulsion between the ions, the number of electrons missing from each ion will be:

(e is the charge on an electron)

1. $\frac{4\pi {\epsilon}_{0}F{d}^{2}}{{e}^{2}}$

2. $\sqrt{\frac{4\pi {\epsilon}_{0}F{d}^{2}}{{d}^{2}}}$

3. $\sqrt{\frac{4\pi {\epsilon}_{0}F{d}^{2}}{{e}^{2}}}$

4. $\frac{4\pi {\epsilon}_{0}F{d}^{2}}{{q}^{2}}$

Subtopic: Coulomb's Law |

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A square surface of side \(L\) (metre) in the plane of the paper is placed in a uniform electric field \(E\) (volt/m) acting along the same plane at an angle θ with the horizontal side of the square as shown in the figure. The electric flux linked to the surface in unit of V-m, is:

1. \(EL^{2}\)

2. \(EL^{2} cos\theta \)

3. \(EL^{2} sin\theta \)

4. \(0\)

Subtopic: Electric Field |

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The electric field at a distance $\frac{3R}{2}$ from the centre of a charged conducting spherical shell of radius R is E. The electric field at a distance $\frac{R}{2}$ from the centre of the sphere is:

1. E

2. $\frac{E}{2}$

3. $\frac{E}{2}$

4. Zero

Subtopic: Gauss's Law |

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The mean free path of electrons in a metal is \(4\times 10^{-8}\) m. The electric field which can give on an average 2 eV energy to an electron in the metal will be:

(Unit: Vm^{-1})

(Unit: Vm

1. \(8\times 10^{7}\)

2. \(5\times 10^{-11}\)

3. \(8\times 10^{-11}\)

4. \(5\times 10^{7}\)

Subtopic: Electric Field |

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A thin conducting ring of radius R is given a charge +Q. The electric field at the centre O of the ring due to the charge on the part AKB of the ring is E. The electric field at the centre due to the charge on the part ACDB of the ring is:

1. 3E along KO

2. E along OK

3. E along KO

4. 3E along OK

Subtopic: Electric Field |

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Three-point charges + q, -2q and +q are placed at points (x=0, y=a, z=0), (x=0, y=0, z=0) and (x=a, y=0, z=0), respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are:

1. | $\sqrt{2}$qa along +y direction |

2. | $\sqrt{2}$qa along the line joining points (x=0, y= 0, z=0) and (x=a, y=a, z=0) |

3. | qa along the line joining points (x=0, y=0, z=0) and (x=a, y=a, z=0) |

4. | $\sqrt{2}$qa along +x direction |

Subtopic: Electric Dipole |

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