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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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The point charges \(8~\mu\text{C}\) and \(-2~\mu\text{C}\) are located at \(x =2~\text{cm}\) and \(x =4~\text{cm},\) respectively on the \(x\)-axis. The ratio of electric flux due to these through two spheres of radii \(3~\text{cm}\) and \(5~\text{cm}\) with their centres at the origin is:
1. \(4:1\)
2. \(3:4\)
3. \(4:3\)
4. \(4:5\)
1. \(4:1\)
2. \(3:4\)
3. \(4:3\)
4. \(4:5\)
Subtopic: Gauss's Law |
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Level 2: 60%+
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A thin ring of radius \(35~\text{cm}\) is uniformly charged with a total charge of \(Q\) coulomb. If the magnitude of the electric field at centre of the half ring is \(100~\text{V/m},\) then the value of \(Q\) is: (in nC)
\(\left(\varepsilon_{o}=8.85 \times 10^{-12} ~\text{C}^2 / \text{Nm}^2 \text { and } \pi=3.14\right)\)
1. \(2.14\)
2. \(2.44\)
3. \(3.25\)
4. \(0.7\)
\(\left(\varepsilon_{o}=8.85 \times 10^{-12} ~\text{C}^2 / \text{Nm}^2 \text { and } \pi=3.14\right)\)
1. \(2.14\)
2. \(2.44\)
3. \(3.25\)
4. \(0.7\)
Subtopic: Gauss's Law |
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Level 2: 60%+
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Two charged conducting spheres \(S_1\) and \(S_2\) of radii \(8~\text{cm}\) and \(18~\text{cm}\) are connected to each other by a wire. After equilibrium is established, the ratio of electric fields on \(S_1\) and \(S_2\) spheres are \({E}_{{S}_ 1}\) and \({E}_{{S}_2}\) respectively. The value of \(\dfrac{{E}_{{S}_1}}{{E}_{{S}_2}}\) is:
1. \(\dfrac{3}{2}\)
2. \(\dfrac{2}{3}\)
3. \(\dfrac{4}{9}\)
4. \(\dfrac{9}{4}\)
1. \(\dfrac{3}{2}\)
2. \(\dfrac{2}{3}\)
3. \(\dfrac{4}{9}\)
4. \(\dfrac{9}{4}\)
Subtopic: Electric Field |
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Level 2: 60%+
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Two short electric dipoles \(A\) \(B\) \(P_1\) \(P_2\) \(x\) \(60^\circ\) \(x\) \(P_2/P_1\)
1. \(\dfrac{\sqrt{3}}{2}\)
2. \(2 \sqrt{3}\)
3. \(\dfrac{1}{\sqrt{3}}\)
4. \(\sqrt{3}\)
1. \(\dfrac{\sqrt{3}}{2}\)
2. \(2 \sqrt{3}\)
3. \(\dfrac{1}{\sqrt{3}}\)
4. \(\sqrt{3}\)
Subtopic: Electric Dipole |
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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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Six point charges are kept \(60^\circ\) apart from each other on the circumference of a circle of radius \(R\) as shown in the figure. The net electric field at the centre of the circle is: (\(\varepsilon_0\) is the permittivity of free space)
1. \(-\dfrac{5 Q}{8 \pi \epsilon_0 R^2}(\hat{i}+\sqrt{3} \hat{j})\)
2. \(-\dfrac{Q}{4 \pi \epsilon_0 R^2}(\sqrt{3} \hat{i}-\hat{j})\)
3. \(-\left(\dfrac{5 Q}{8 \pi \epsilon_o R^2}\right)(\hat{i}-3 \hat{j})~\)
4. \(\dfrac{Q}{4 \pi \epsilon_0 R^2}(\sqrt{3} \hat{i}-\hat{j})\)
1. \(-\dfrac{5 Q}{8 \pi \epsilon_0 R^2}(\hat{i}+\sqrt{3} \hat{j})\)
2. \(-\dfrac{Q}{4 \pi \epsilon_0 R^2}(\sqrt{3} \hat{i}-\hat{j})\)
3. \(-\left(\dfrac{5 Q}{8 \pi \epsilon_o R^2}\right)(\hat{i}-3 \hat{j})~\)
4. \(\dfrac{Q}{4 \pi \epsilon_0 R^2}(\sqrt{3} \hat{i}-\hat{j})\)
Subtopic: Electric Field |
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Level 1: 80%+
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A simple pendulum has a bob with mass \(m\) and charge \(q\). The pendulum string has negligible mass. When a uniform and horizontal electric field \(\vec{E}\)is applied, the tension in the string changes. The final tension in the string, when pendulum attains an equilibrium position is:
(\(g\): acceleration due to gravity)
1. \(mg-qE\)
2. \(mg+qE\)
3. \(\sqrt{m^2g^2+q^2E^2}\)
4. \(\sqrt{m^2g^2-q^2E^2}\)
(\(g\): acceleration due to gravity)
1. \(mg-qE\)
2. \(mg+qE\)
3. \(\sqrt{m^2g^2+q^2E^2}\)
4. \(\sqrt{m^2g^2-q^2E^2}\)
Subtopic: Electric Field |
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Level 1: 80%+
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Two point charges \(2q\) and \(q\) are placed at vertex \(A\) and centre of face \(CDEF\) of the cube as shown in figure. The electric flux passing through the cube is:
1. \(\dfrac{3 q}{\varepsilon_0}\)
2. \(\dfrac{{q}}{\varepsilon_0}\)
3. \(\dfrac{3 q}{2 \varepsilon_0}\)
4. \(\dfrac{3 q}{4 \varepsilon_0}\)
1. \(\dfrac{3 q}{\varepsilon_0}\)
2. \(\dfrac{{q}}{\varepsilon_0}\)
3. \(\dfrac{3 q}{2 \varepsilon_0}\)
4. \(\dfrac{3 q}{4 \varepsilon_0}\)
Subtopic: Gauss's Law |
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Level 1: 80%+
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Two shorts dipoles \((A,B),\) \(A\) having charges \(\pm 2~ \mu \text{C}\) and length \(1~\text{cm}\) and \(B\) having charges \(\pm 4~ \mu \text{C}\) and length \(1~\text{cm}\) are placed with their centres \(80~\text{cm}\) apart as shown in the figure. The electric field at a point \(P\), equi-distant from the centres of both dipoles is: (in N/C)
1. \(\dfrac{9}{16} \sqrt{2} \times 10^5\)
2. \(4.5 \sqrt{2} \times 10^4\)
3. \(9 \sqrt{2} \times 10^4\)
4. \(\dfrac{9}{16} \sqrt{2} \times 10^4\)
1. \(\dfrac{9}{16} \sqrt{2} \times 10^5\)
2. \(4.5 \sqrt{2} \times 10^4\)
3. \(9 \sqrt{2} \times 10^4\)
4. \(\dfrac{9}{16} \sqrt{2} \times 10^4\)
Subtopic: Electric Dipole |
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