03. ELECTRIC FIELD
Electric Charges and Fields

267948 A particle having charge that on an electron and mass \(1.6 \times 10^{-30} \mathrm{~kg}\) is projected with an initial speed ' \(u\) ' to the horizontal from the lower plate of a parallel plate capacitor as shown. The plates are sufficiently long and have separation \(2 \mathrm{~cm}\). Then the maximum value of velocity of particle not to hit the upper plate. ( \(\mathrm{E}=10^{3} \mathrm{~V} / \mathrm{m}\) upwards).

1 \(2 x 10^6 m/s\)
2 \(4 x 10^6 m/s\)
3 \(6 x 10^6 m/s\)
4 \(3x 10^6 m/s\)
Electric Charges and Fields

267949 An electric field is acting vertically upwards. A small body of mass\(1 \mathrm{gm}\) and charge \(-1 \mu \mathrm{C}\) is projected with a velocity \(10 \mathrm{~m} / \mathrm{s}\) at an angle \(45^{\circ}\) with horizontal. Its horizontal range is \(2 \mathrm{~m}\) then theintensity of electric field is : \((\mathrm{g}=10 \mathrm{~m} /\) \(\mathbf{s}^{2}\) )

1 \(20,000 \mathrm{~N} / \mathrm{C}\)
2 \(10,000 \mathrm{~N} / \mathrm{C}\)
3 \(40,000 \mathrm{~N} / \mathrm{C}\)
4 \(90,000 \mathrm{~N} / \mathrm{C}\)
Electric Charges and Fields

267950 A thin copper ring of radius '\(a\) ' is charged with \(q\) units of electricity. An electron is placed at the centre of the copper ring. If the electron is displaced a little, it will have frequency.

1 \(\frac{1}{2 \pi} \sqrt{\frac{e q}{4 \pi \epsilon_{0} m a^{3}}}\)
2 \(\frac{1}{2 \pi} \sqrt{\frac{q}{4 \pi \epsilon_{0} e m a^{3}}}\)
3 \(\sqrt{\frac{e q}{4 \pi \epsilon_{0} m a}}\)
4 \(\sqrt{\frac{q}{4 \pi \epsilon_{0} e m a^{3}}}\)
Electric Charges and Fields

267951 A thin fixed ring of radius 1metre has a positivecharge \(1 \times 10^{-5} \mathrm{C}\) uniformly distributed over it. A particle of mass \(0.9 \mathrm{gm}\) and having a negative charge of \(1 \times 10^{-6} \mathrm{C}\) is placed on the axis at a distance of \(1 \mathrm{~cm}\) from the centre of the ring. Assuming that the oscillations have small amplitude, the time period of oscillations is

1 \(0.23 \mathrm{~s}\)
2 \(0.39 \mathrm{~s}\)
3 \(0.49 \mathrm{~s}\)
4 \(0.63 \mathrm{~s}\)
Electric Charges and Fields

267948 A particle having charge that on an electron and mass \(1.6 \times 10^{-30} \mathrm{~kg}\) is projected with an initial speed ' \(u\) ' to the horizontal from the lower plate of a parallel plate capacitor as shown. The plates are sufficiently long and have separation \(2 \mathrm{~cm}\). Then the maximum value of velocity of particle not to hit the upper plate. ( \(\mathrm{E}=10^{3} \mathrm{~V} / \mathrm{m}\) upwards).

1 \(2 x 10^6 m/s\)
2 \(4 x 10^6 m/s\)
3 \(6 x 10^6 m/s\)
4 \(3x 10^6 m/s\)
Electric Charges and Fields

267949 An electric field is acting vertically upwards. A small body of mass\(1 \mathrm{gm}\) and charge \(-1 \mu \mathrm{C}\) is projected with a velocity \(10 \mathrm{~m} / \mathrm{s}\) at an angle \(45^{\circ}\) with horizontal. Its horizontal range is \(2 \mathrm{~m}\) then theintensity of electric field is : \((\mathrm{g}=10 \mathrm{~m} /\) \(\mathbf{s}^{2}\) )

1 \(20,000 \mathrm{~N} / \mathrm{C}\)
2 \(10,000 \mathrm{~N} / \mathrm{C}\)
3 \(40,000 \mathrm{~N} / \mathrm{C}\)
4 \(90,000 \mathrm{~N} / \mathrm{C}\)
Electric Charges and Fields

267950 A thin copper ring of radius '\(a\) ' is charged with \(q\) units of electricity. An electron is placed at the centre of the copper ring. If the electron is displaced a little, it will have frequency.

1 \(\frac{1}{2 \pi} \sqrt{\frac{e q}{4 \pi \epsilon_{0} m a^{3}}}\)
2 \(\frac{1}{2 \pi} \sqrt{\frac{q}{4 \pi \epsilon_{0} e m a^{3}}}\)
3 \(\sqrt{\frac{e q}{4 \pi \epsilon_{0} m a}}\)
4 \(\sqrt{\frac{q}{4 \pi \epsilon_{0} e m a^{3}}}\)
Electric Charges and Fields

267951 A thin fixed ring of radius 1metre has a positivecharge \(1 \times 10^{-5} \mathrm{C}\) uniformly distributed over it. A particle of mass \(0.9 \mathrm{gm}\) and having a negative charge of \(1 \times 10^{-6} \mathrm{C}\) is placed on the axis at a distance of \(1 \mathrm{~cm}\) from the centre of the ring. Assuming that the oscillations have small amplitude, the time period of oscillations is

1 \(0.23 \mathrm{~s}\)
2 \(0.39 \mathrm{~s}\)
3 \(0.49 \mathrm{~s}\)
4 \(0.63 \mathrm{~s}\)
Electric Charges and Fields

267948 A particle having charge that on an electron and mass \(1.6 \times 10^{-30} \mathrm{~kg}\) is projected with an initial speed ' \(u\) ' to the horizontal from the lower plate of a parallel plate capacitor as shown. The plates are sufficiently long and have separation \(2 \mathrm{~cm}\). Then the maximum value of velocity of particle not to hit the upper plate. ( \(\mathrm{E}=10^{3} \mathrm{~V} / \mathrm{m}\) upwards).

1 \(2 x 10^6 m/s\)
2 \(4 x 10^6 m/s\)
3 \(6 x 10^6 m/s\)
4 \(3x 10^6 m/s\)
Electric Charges and Fields

267949 An electric field is acting vertically upwards. A small body of mass\(1 \mathrm{gm}\) and charge \(-1 \mu \mathrm{C}\) is projected with a velocity \(10 \mathrm{~m} / \mathrm{s}\) at an angle \(45^{\circ}\) with horizontal. Its horizontal range is \(2 \mathrm{~m}\) then theintensity of electric field is : \((\mathrm{g}=10 \mathrm{~m} /\) \(\mathbf{s}^{2}\) )

1 \(20,000 \mathrm{~N} / \mathrm{C}\)
2 \(10,000 \mathrm{~N} / \mathrm{C}\)
3 \(40,000 \mathrm{~N} / \mathrm{C}\)
4 \(90,000 \mathrm{~N} / \mathrm{C}\)
Electric Charges and Fields

267950 A thin copper ring of radius '\(a\) ' is charged with \(q\) units of electricity. An electron is placed at the centre of the copper ring. If the electron is displaced a little, it will have frequency.

1 \(\frac{1}{2 \pi} \sqrt{\frac{e q}{4 \pi \epsilon_{0} m a^{3}}}\)
2 \(\frac{1}{2 \pi} \sqrt{\frac{q}{4 \pi \epsilon_{0} e m a^{3}}}\)
3 \(\sqrt{\frac{e q}{4 \pi \epsilon_{0} m a}}\)
4 \(\sqrt{\frac{q}{4 \pi \epsilon_{0} e m a^{3}}}\)
Electric Charges and Fields

267951 A thin fixed ring of radius 1metre has a positivecharge \(1 \times 10^{-5} \mathrm{C}\) uniformly distributed over it. A particle of mass \(0.9 \mathrm{gm}\) and having a negative charge of \(1 \times 10^{-6} \mathrm{C}\) is placed on the axis at a distance of \(1 \mathrm{~cm}\) from the centre of the ring. Assuming that the oscillations have small amplitude, the time period of oscillations is

1 \(0.23 \mathrm{~s}\)
2 \(0.39 \mathrm{~s}\)
3 \(0.49 \mathrm{~s}\)
4 \(0.63 \mathrm{~s}\)
Electric Charges and Fields

267948 A particle having charge that on an electron and mass \(1.6 \times 10^{-30} \mathrm{~kg}\) is projected with an initial speed ' \(u\) ' to the horizontal from the lower plate of a parallel plate capacitor as shown. The plates are sufficiently long and have separation \(2 \mathrm{~cm}\). Then the maximum value of velocity of particle not to hit the upper plate. ( \(\mathrm{E}=10^{3} \mathrm{~V} / \mathrm{m}\) upwards).

1 \(2 x 10^6 m/s\)
2 \(4 x 10^6 m/s\)
3 \(6 x 10^6 m/s\)
4 \(3x 10^6 m/s\)
Electric Charges and Fields

267949 An electric field is acting vertically upwards. A small body of mass\(1 \mathrm{gm}\) and charge \(-1 \mu \mathrm{C}\) is projected with a velocity \(10 \mathrm{~m} / \mathrm{s}\) at an angle \(45^{\circ}\) with horizontal. Its horizontal range is \(2 \mathrm{~m}\) then theintensity of electric field is : \((\mathrm{g}=10 \mathrm{~m} /\) \(\mathbf{s}^{2}\) )

1 \(20,000 \mathrm{~N} / \mathrm{C}\)
2 \(10,000 \mathrm{~N} / \mathrm{C}\)
3 \(40,000 \mathrm{~N} / \mathrm{C}\)
4 \(90,000 \mathrm{~N} / \mathrm{C}\)
Electric Charges and Fields

267950 A thin copper ring of radius '\(a\) ' is charged with \(q\) units of electricity. An electron is placed at the centre of the copper ring. If the electron is displaced a little, it will have frequency.

1 \(\frac{1}{2 \pi} \sqrt{\frac{e q}{4 \pi \epsilon_{0} m a^{3}}}\)
2 \(\frac{1}{2 \pi} \sqrt{\frac{q}{4 \pi \epsilon_{0} e m a^{3}}}\)
3 \(\sqrt{\frac{e q}{4 \pi \epsilon_{0} m a}}\)
4 \(\sqrt{\frac{q}{4 \pi \epsilon_{0} e m a^{3}}}\)
Electric Charges and Fields

267951 A thin fixed ring of radius 1metre has a positivecharge \(1 \times 10^{-5} \mathrm{C}\) uniformly distributed over it. A particle of mass \(0.9 \mathrm{gm}\) and having a negative charge of \(1 \times 10^{-6} \mathrm{C}\) is placed on the axis at a distance of \(1 \mathrm{~cm}\) from the centre of the ring. Assuming that the oscillations have small amplitude, the time period of oscillations is

1 \(0.23 \mathrm{~s}\)
2 \(0.39 \mathrm{~s}\)
3 \(0.49 \mathrm{~s}\)
4 \(0.63 \mathrm{~s}\)