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Q. No.An electron (charge: \(e\) & mass: \(m\)) emitted from the positive plate \(A\) of the capacitor \(AB\), just manages to reach the negative plate \(B\). If the potential difference between the plates is \(V_0\), then the speed of the electron when it is emitted is:
1.
\(\sqrt{\frac{e V_{0}}{m}} \quad\)
2.
\(\sqrt{\frac{e V_{0}}{2 m}} \quad\)
3.
\(\sqrt{\frac{2 e V_{0}}{m}}\)
4.
\(\sqrt{\frac{2 e V_{0} d}{m}}\)
Subtopic: Electric Potential Energy |
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Two charges \(q,\) \(-q\) are placed at the two ends of the hypotenuse of an isosceles right-angled triangle, the smaller sides being of length, \(a.\) A dipole of dipole moment \(p\) is placed at the right-angled vertex with its axis pointing towards the positive charge, \(q.\) The torque acting on the dipole is:
1. \(\dfrac{kpq}{a^2}\)
2. zero
3. \(\dfrac{2kpq}{a^2}\)
4. \(\dfrac{\sqrt{5}kpq}{a^2}\)
Subtopic: Energy of Dipole in an External Field |
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A sector of a circle (radius: R) carries a uniform surface charge Q distributed over it. The potential, due to this charge, at the center of curvature if the sector (o) is
1. \(\frac{kQ}{R}\)
2. \(\frac{kQ}{2R}\)
3. \(\frac{2kQ}{R}\)
4. \(\frac{kQ}{R}ln~2\)
1. \(\frac{kQ}{R}\)
2. \(\frac{kQ}{2R}\)
3. \(\frac{2kQ}{R}\)
4. \(\frac{kQ}{R}ln~2\)
Subtopic: Electric Potential |
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Two identical capacitors, each of capacitance \(C\), are connected in series and are charged by means of an ideal battery of emf \(E\). They are disconnected and reconnected in parallel and connected to the same battery. During this reconnection, the positive terminals of the capacitors are connected to the positive terminal of the battery and their negative terminals are similarly connected together. Let, the work done by the battery during the first connection be \(W_1\), and during the second be \(W_2\). Then,
| 1. | \(W_1=W_2\) | 2. | \(2W_1 =W_2\) |
| 3. | \(W_1 = 2W_2\) | 4. | \(4W_1 = W_2\) |
Subtopic: Energy stored in Capacitor |
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A semi-circular wire carries a positive charge \(Q\) distributed uniformly over its circumference, and lies with its center at the origin and its ends on the x-axis, as shown in the figure. A single point charge is to be placed so that the net electric field due to the charge \(Q\) and the new charge \((q_1)\) is zero at the origin. Let the distance of \(q_1\) from O be \(r_1\). The potential at the origin is also zero. Which of the following is correct?
\(1.~ r_{1}< \frac{r}{2} \\ 2.~ \frac{r}{2}<r_{1}< r \\ 3.~ r<r_{1}<\frac{3 r}{2}\\ 4.~ \frac{3 r}{2}<r_{1}\)
\(1.~ r_{1}< \frac{r}{2} \\ 2.~ \frac{r}{2}<r_{1}< r \\ 3.~ r<r_{1}<\frac{3 r}{2}\\ 4.~ \frac{3 r}{2}<r_{1}\)
Subtopic: Electric Potential |
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A \(12 ~\mu \text{F}\) capacitor is charged by means of a \(6~\text{V}\) battery and the charged capacitor and the battery are connected in series so that their combined potential difference is twice as much. When a second unknown capacitor (initially uncharged) is connected across this combination, the first capacitor is observed to lose half of its initial charge.
The capacitance of the unknown capacitor is:
1. \(4 ~\mu \text{F}\)
2. \(6~ \mu \text{F}\)
3. \(24 ~\mu \text{F}\)
4. \(36 ~\mu \text{F}\)
The capacitance of the unknown capacitor is:
1. \(4 ~\mu \text{F}\)
2. \(6~ \mu \text{F}\)
3. \(24 ~\mu \text{F}\)
4. \(36 ~\mu \text{F}\)
Subtopic: Capacitance |
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An arrangement consisting of two concentric spherical shells A and B has a capacitance \(C_0\) between them. If the upper 'hemispherical' space between them is filled by a dielectric of relative permittivity \(K_1\) and the lower by one of relative permittivity \(K_2,\) the new capacitance will be:
| 1. | \(\left(K_{1}+K_{2}\right) C_{0}\) | 2. | \( \dfrac{K_{1}+K_{2}}{2} C_{0}\) |
| 3. | \(\dfrac{1}{2}\left(\dfrac{1}{K_{1}}+\dfrac{1}{K_{2}}\right) C_{0}\) | 4. | \( \dfrac{2 K_{1} K_{2}}{K_{1}+K_{2}} C_{0}\) |
Subtopic: Dielectrics in Capacitors |
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A uniform electric field exists in a certain region of space. The potential at the following points are given (all units are in SI):
• \(A \left ( 1, 0, 0 \right )\) \(V_{A}=2\) volt
• \(B \left ( 0, 2, 0 \right )\) \(V_{B}=4\) volt
• \(C \left ( 0, 0, 2 \right )\) \(V_{C}=6\) volt
• \(D \left ( 1, 1, 0 \right )\) \(V_{D}=-1\) volt
The component of the electric field along the \(x\text-\)axis is:
1. \(2\) V/m
2. \(8\) V/m
3. \(3\) V/m
4. \(-6\) V/m
• \(A \left ( 1, 0, 0 \right )\) \(V_{A}=2\) volt
• \(B \left ( 0, 2, 0 \right )\) \(V_{B}=4\) volt
• \(C \left ( 0, 0, 2 \right )\) \(V_{C}=6\) volt
• \(D \left ( 1, 1, 0 \right )\) \(V_{D}=-1\) volt
The component of the electric field along the \(x\text-\)axis is:
1. \(2\) V/m
2. \(8\) V/m
3. \(3\) V/m
4. \(-6\) V/m
Subtopic: Relation between Field & Potential |
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The arrangement shown in the figure is set up with capacitors initially uncharged, and the circuit is completed. A potential difference is imposed across \(AB\) so that the charge on the upper capacitor is doubled without changing its sign.
Then, \(V_{A}-V_{B}=\)
1. \(E_0\)
2. \(2E_0\)
3. \(-E_0\)
4. zero
Then, \(V_{A}-V_{B}=\)
1. \(E_0\)
2. \(2E_0\)
3. \(-E_0\)
4. zero
Subtopic: Capacitance |
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Three metallic spheres of radii \(r_1,~ r_2,~ r_3\) are connected by very long conducting wires to form an equilateral triangle. The capacitance of the system is:
1. \(4 \pi \varepsilon_{0}\left(r_{1}+r_{2}+r_{3}\right)\)
2. \(4 \pi \varepsilon_{0} \dfrac{r_{1}^{2}+r_{2}^{2}+r_{3}^{2}}{r_{1}+r_{2}+r_{3}}\)
3. \(4 \pi \varepsilon_{0}\left(\dfrac{1}{r_{1}}+\dfrac{1}{r_{2}}+\dfrac{1}{r_{3}}\right)^{-1}\)
4. \(4 \pi \varepsilon_{0} \sqrt{r_{1}^{2}+r_{2}^{2}+r_{3}^{2}}\)
1. \(4 \pi \varepsilon_{0}\left(r_{1}+r_{2}+r_{3}\right)\)
2. \(4 \pi \varepsilon_{0} \dfrac{r_{1}^{2}+r_{2}^{2}+r_{3}^{2}}{r_{1}+r_{2}+r_{3}}\)
3. \(4 \pi \varepsilon_{0}\left(\dfrac{1}{r_{1}}+\dfrac{1}{r_{2}}+\dfrac{1}{r_{3}}\right)^{-1}\)
4. \(4 \pi \varepsilon_{0} \sqrt{r_{1}^{2}+r_{2}^{2}+r_{3}^{2}}\)
Subtopic: Capacitance |
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