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A toy car with charge \(q\) moves on a frictionless horizontal plane surface under the influence of a uniform electric field \(\vec E.\)Due to the force \(q\vec E,\) its velocity increases from \(0\) to \(6~\text{m/s}\) in a one-second duration. At that instant, the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between \(0\) to \(3\) seconds are respectively:

1. \(2~\text{m/s}, ~4~\text{m/s}\)

2. \(1~\text{m/s}, ~3~\text{m/s}\)

3. \(1~\text{m/s}, ~3.5~\text{m/s}\)

4. \(1.5~\text{m/s},~ 3~\text{m/s}\)

Subtopic: Electric Field |

63%

From NCERT

NEET - 2018

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Two identical charged spheres suspended from a common point by two massless strings of lengths \(l,\) are initially at a distance \(d\) \(\left ( d\ll l \right )\) apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity \(v.\) Then, \(v\) varies as a function of the distance \(x\) between the sphere, as:

1. \(v\propto x\)

2. \(v\propto x^{-1/2}\)

3. \(v\propto x^{-1}\)

4. \(v\propto x^{1/2}\)

1. \(v\propto x\)

2. \(v\propto x^{-1/2}\)

3. \(v\propto x^{-1}\)

4. \(v\propto x^{1/2}\)

Subtopic: Coulomb's Law |

78%

From NCERT

NEET - 2016

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

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

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

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

Subtopic: Gauss's Law |

67%

From NCERT

NEET - 2015

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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

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 |

70%

From NCERT

AIPMT - 2013

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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. \(\frac{2q}{\varepsilon_0}\)

2. \(\frac{q}{8\varepsilon_0}\)

3. \(\frac{q}{\varepsilon_0}\)

4. \(\frac{q}{2\varepsilon_0}\)

Subtopic: Gauss's Law |

88%

From NCERT

AIPMT - 2012

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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 |

Subtopic: Gauss's Law |

88%

From NCERT

AIPMT - 2011

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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. | \(\frac{4 \pi \varepsilon_{0} F d^{2}}{e^{2}}\) | 2. | \(\sqrt{\frac{4 \pi \varepsilon_{0} F d^{2}}{d^{2}}}\) |

3. | \(\sqrt{\frac{4 \pi \varepsilon_{0} F d^{2}}{e^{2}}}\) | 4. | \(\frac{4 \pi \varepsilon_{0} F d^{2}}{q^{2}}\) |

Subtopic: Coulomb's Law |

77%

From NCERT

AIPMT - 2010

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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 the unit of V-m is:

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

3. | \(EL^{2} sin\theta \) | 4. | \(0\) |

Subtopic: Electric Field |

75%

From NCERT

AIPMT - 2010

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The mean free path of electrons in a metal is \(4\times 10^{-8}~\text{m}\). The electric field which can give an average of \(2~\text{eV}\) energy to an electron in the metal will be in units of Vm^{-1}:

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

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

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

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

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

Subtopic: Electric Field |

From NCERT

AIPMT - 2009

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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 |

75%

From NCERT

AIPMT - 2008

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