Q. No.The metal plates \((A, B)\) are kept horizontally with separation of \(\left(\dfrac{12}{\pi}\right) ~\text{cm},\) with plate \(A\) on the top. An atomizer jet sprays oil (density \(1.5~\text{g/cm}^{3}\)) droplets or radius \(1~\text{mm}\) horizontally. All oil droplets carry a charge \(5~\text{nC}.\) The potentials \(V_A\) and \(V_B\) are required on plates \(A\) and \(B\) respectively in order to ensure the droplets do not descend. The value of \(V_A\) and \(V_B\) are:
(Neglect the air resistance to the droplets and take \(g =10~\text{m/s}^{2}\))
1. \(100~\text{V and}~ 580 ~\text{V}\)
2. \(580~\text{V and}~ 100 ~\text{V}\)
3. \(60~\text{V and}~ 400 ~\text{V}\)
4. \(0~\text{V and} ~-200~\text{V}\)
(Neglect the air resistance to the droplets and take \(g =10~\text{m/s}^{2}\))
1. \(100~\text{V and}~ 580 ~\text{V}\)
2. \(580~\text{V and}~ 100 ~\text{V}\)
3. \(60~\text{V and}~ 400 ~\text{V}\)
4. \(0~\text{V and} ~-200~\text{V}\)
Subtopic: Coulomb's Law |
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Two point charges \(q_1=3~ \mu \text{C} \text { and } q_2=-4~ \mu\text{C}\) are placed at points \((2 \hat{i}+3 \hat{j}+3 \hat{k})\) and \((\hat{i}+\hat{j}+\hat{k})\) respectively. Force on charge \(q_2\) is: (in N) \(\left(\text { Take } \dfrac{1}{4 \pi \epsilon_0}=9 \times 10^9 \text { SI Units }\right)~\)
1. \((12 \hat{i}+24 \hat{j}+24 \hat{k}) \times 10^{-3}\)
2. \((4 \hat{i}+8 \hat{j}+8 \hat{k}) \times 10^{-3}\)
3. \((3 \hat{i}+6 \hat{j}+6 \hat{k}) \times 10^{-3}\)
4. \((-4 \hat{i}-8 \hat{j}-8 \hat{k}) \times 10^{-3}\)
1. \((12 \hat{i}+24 \hat{j}+24 \hat{k}) \times 10^{-3}\)
2. \((4 \hat{i}+8 \hat{j}+8 \hat{k}) \times 10^{-3}\)
3. \((3 \hat{i}+6 \hat{j}+6 \hat{k}) \times 10^{-3}\)
4. \((-4 \hat{i}-8 \hat{j}-8 \hat{k}) \times 10^{-3}\)
Subtopic: Coulomb's Law |
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Level 3: 35%-60%
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A point charge \(q=1 ~\mu \text{C}\) is located at a distance \(2~\text{cm}\) from one end of a thin insulating wire of length \(10~\text{cm}\) having a charge \(Q=24~ \mu \text{C},\) distributed uniformly along its length, as shown in figure. Force between \(q \) and wire is: (in N)
\(\text { (Use } \dfrac{1}{4 \pi \epsilon_0}=9 \times 10^9 ~\text{N} \cdot \text{m}^2 / \text{C}^2 \text { ) }\)
1. \(90\)
2. \(40\)
3. \(100\)
4. \(120\)
\(\text { (Use } \dfrac{1}{4 \pi \epsilon_0}=9 \times 10^9 ~\text{N} \cdot \text{m}^2 / \text{C}^2 \text { ) }\)
1. \(90\)
2. \(40\)
3. \(100\)
4. \(120\)
Subtopic: Coulomb's Law |
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Level 2: 60%+
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A small uncharged conducting sphere is placed in contact with an identical sphere but having \(4×10^-8~\text {C}\) charge and then removed to a distance such that the force of repulsion between them is \(9×10^{-3}~\text {N}.\) The distance between them is (Take \(\dfrac{1}{4πε_0}\) as \(9 × 10^9 \) in \(\text{SI units})\)
1. \(2~\text{cm}\)
2. \(3~\text{cm}\)
3. \(1~\text{cm}\)
4. \(4~\text{cm}\)
1. \(2~\text{cm}\)
2. \(3~\text{cm}\)
3. \(1~\text{cm}\)
4. \(4~\text{cm}\)
Subtopic: Coulomb's Law |
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Level 1: 80%+
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Two identical conducting spheres \(P\) and \(S\) with charge \(Q\) on each, repel each other with a force \(16~\text N.\) A third identical uncharged conducting sphere \(R\) is successively brought in contact with the two spheres. The new force of repulsion between \(P\) and \(S\) is :
1. 4 N
2. 1 N
3. 6 N
4. 12 N
Subtopic: Coulomb's Law |
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Two identical charged particles are suspended from a common point by light, inextensible threads, as shown in the figure. Due to electrostatic repulsion, the threads make equal angles \(\theta\) with the vertical. When the entire arrangement is immersed in a liquid, the angular separation between the two particles remains unchanged. The relative density of the particles is \(1.4,\) and the relative density of the liquid is \(0.7\cdot\) The dielectric constant of the liquid is:
| 1. | \(5\) | 2. | \(2\) |
| 3. | \(3\) | 4. | \(1\) |
Subtopic: Coulomb's Law |
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Level 2: 60%+
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A ring of radius \(3 ~\text{cm}\) carries a uniformly distributed charge of \(2\pi~\text{C}.\) A point charge of \(10^{-6}~\text{C}\) is placed at its centre. What is the tension developed in the ring due to electrostatic repulsion?
| 1. | \(10^{13}~\text N\) | 2. | \(10^{5}~\text N\) |
| 3. | \(10^{7}~\text N\) | 4. | \(10^{11}~\text {N}\) |
Subtopic: Coulomb's Law |
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The force between two charged particles placed in the air at separation \(x\) is \(F_0.\) Both the charged particles immersed in a medium of dielectric constant \(K\) without changing the separation between two charges, then the net force on one of the particles is:
| 1. | \( \dfrac{F_0}{K}\) | 2. | \(\dfrac{F_0}{2K}\) |
| 3. | \(\dfrac{2F_0}{K}\) | 4. | \(F_0\) |
Subtopic: Coulomb's Law |
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An electron and a proton are placed at a certain distance apart. Then the ratio of coulombs force and gravitational force is:
1. \(10^{32}\)
2. \(10^{39}\)
3. \(10^{36}\)
4. \(10^{42}\)
1. \(10^{32}\)
2. \(10^{39}\)
3. \(10^{36}\)
4. \(10^{42}\)
Subtopic: Coulomb's Law |
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A charge of \(10~\mu \text{C}\) is split into two equal parts, and the resulting charges are placed \(1~\text{cm}\) apart. What will be the force of repulsion between the two charges?
| 1. | \(225\) N | 2. | \(450\) N |
| 3. | \(2250\) N | 4. | \(4500\) N |
Subtopic: Coulomb's Law |
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Level 1: 80%+
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