Q. No.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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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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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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Identify the correct statements:
Choose the correct answer from the options given below:
1. \(\mathrm{A,B,D,E}~\text{only}\)
2. \(\mathrm{A,B,C,D}~\text{only}\)
3. \(\mathrm{B,C,D,E}~\text{only}\)
4. \(\mathrm{A,C,E}~\text{only}\)
| \(\mathrm{A}.\) | Electrostatic field lines form closed loops. |
| \(\mathrm{B}.\) | The electric field lines point radially outward when charge is greater than zero. |
| \(\mathrm{C}.\) | The Gauss-Law is valid only for inverse-square force. |
| \(\mathrm{D}.\) | The work done in moving a charged particle in a static electric field around a closed path is zero. |
| \(\mathrm{E}.\) | The motion of a particle under Coulomb’s force must take place in a plane. |
1. \(\mathrm{A,B,D,E}~\text{only}\)
2. \(\mathrm{A,B,C,D}~\text{only}\)
3. \(\mathrm{B,C,D,E}~\text{only}\)
4. \(\mathrm{A,C,E}~\text{only}\)
Subtopic: Electric Field |
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A metallic ring is uniformly charged as shown in figure. \(AC\) and \(BD\) are two mutually perpendicular diameters. Electric field due to arc \(AB\) at \(O\) is \(E\) in magnitude. What would be the magnitude of electric field at \(O\) due to an arc \(ABC~\)?
1. Zero
2. \(2E\)
3. \(\dfrac{E}{2}\)
4. \(\sqrt{2}E\)
1. Zero
2. \(2E\)
3. \(\dfrac{E}{2}\)
4. \(\sqrt{2}E\)
Subtopic: Electric Field |
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Two infinite identical charged sheets and a charged spherical body of charge density \(\rho\) are arranged as shown in figure. Then the correct relation between the electrical fields at \(A, B, C \) and \(D \) points is:
1. \(\left|\vec{E}_A\right|=\left|\vec{E}_B\right| ; \vec{E}_C>\vec{E}_D \)
2. \(\vec{E}_C \neq \vec{E}_D ; \vec{E}_A>\vec{E}_B\)
3. \(\vec{E}_A=\vec{E}_B ; \vec{E}_C=\vec{E}_D\)
4. \(\vec{E}_A>\vec{E}_B ; \vec{E}_C=\vec{E}_D \)
1. \(\left|\vec{E}_A\right|=\left|\vec{E}_B\right| ; \vec{E}_C>\vec{E}_D \)
2. \(\vec{E}_C \neq \vec{E}_D ; \vec{E}_A>\vec{E}_B\)
3. \(\vec{E}_A=\vec{E}_B ; \vec{E}_C=\vec{E}_D\)
4. \(\vec{E}_A>\vec{E}_B ; \vec{E}_C=\vec{E}_D \)
Subtopic: Electric Field |
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Given below are two statements:
In the light of the above statements. choose the most appropriate answer from the options given below:
| Assertion (A): | The outer body of an air craft is made of metal which protects persons sitting inside from lightning-strikes. |
| Reason (R): | The electric field inside the cavity enclose by a conductor is zero. |
In the light of the above statements. choose the most appropriate answer from the options given below:
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
Subtopic: Electric Field |
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Consider a circular loop that is uniformly charged and has a radius \(a\sqrt2. \) Find the position along the positive \(z\text-\)axis of the Cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in \(x\text-y \) plane at the origin:
1. \(\dfrac{a}{\sqrt{2} }\)
2. \(\dfrac{a}{2} \)
3. \(0\)
4. \(a \)
1. \(\dfrac{a}{\sqrt{2} }\)
2. \(\dfrac{a}{2} \)
3. \(0\)
4. \(a \)
Subtopic: Electric Field |
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Consider two infinitely large plane parallel conducting plates as shown below. The plates are uniformly charged with a surface charge density \(+\sigma \) and \(-2\sigma ~\). The force experienced by a point charge \(+q ~\) placed at the midpoint between two plates will be:
1. \(\dfrac{\sigma q}{4 \varepsilon_0}\)
2. \(\dfrac{\sigma q}{2 \varepsilon_0}\)
3. \(\dfrac{3\sigma q}{2 \varepsilon_0}\)
4. \(\dfrac{3\sigma q}{4 \varepsilon_0}\)
1. \(\dfrac{\sigma q}{4 \varepsilon_0}\)
2. \(\dfrac{\sigma q}{2 \varepsilon_0}\)
3. \(\dfrac{3\sigma q}{2 \varepsilon_0}\)
4. \(\dfrac{3\sigma q}{4 \varepsilon_0}\)
Subtopic: Electric Field |
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A point charge \(+q \) is placed at the origin. A second point charge \(+9q \) is placed at \((d,0,0) \) in cartesian coordinate system. The point in between them where the electric field vanishes is:
1. \(\left ( \dfrac d4,0,0 \right) ~\)
2. \(\left ( \dfrac d3,0,0 \right) ~\)
3. \(\left ( \dfrac {4d}{3},0,0 \right) ~\)
4. \(\left ( \dfrac {3d}{4},0,0 \right) ~\)
1. \(\left ( \dfrac d4,0,0 \right) ~\)
2. \(\left ( \dfrac d3,0,0 \right) ~\)
3. \(\left ( \dfrac {4d}{3},0,0 \right) ~\)
4. \(\left ( \dfrac {3d}{4},0,0 \right) ~\)
Subtopic: Electric Field |
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