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Q. No.The left half of a parallel plate capacitor is filled with a dielectric of relative permittivity \(K\) while the right half is filled with air. The capacitor is charged by connecting its plates to a battery. The electric field within the dielectric is \(E_K\) and that within the air is \(E.\) Which, of the following, is true?
| 1. | \(E_K=E\) | 2. | \({\Large\frac{E_K}{E}}=K\) |
| 3. | \({\Large\frac{E_K}{E}}={\large\frac{1}{K}}\) | 4. | \({\Large\frac{E_K}{E}}=\sqrt K\) |
Subtopic: Dielectrics in Capacitors |
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The capacitance between a pair of identical conducting parallel plates \((A~\&~B),\) placed close together, is \(20\) nF (Fig I). An identical third conducting plate \((C)\) is placed parallel to the other two (Fig. II), so that they form an equidistant system of parallel plates. Plates \(A,C\) are connected by a conducting wire. The capacitance between \(A,B\) is now:
| 1. | \(10\) nF | 2. | \(20\) nF |
| 3. | \(40\) nF | 4. | none of the above |
Subtopic: Combination of Capacitors |
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Identical charges are distributed uniformly on the surfaces of a sphere and a disc of the same radius. The potential at the centre of the sphere is \(V_1,\) and the potential at the centre of the disc is \(V_2.\) The ratio \(\dfrac{V_2}{V_1}\) will be equal to:
| 1. | \(1\) | 2. | \(2\) |
| 3. | \(4\) | 4. | \(\sqrt2\) |
Subtopic: Electric Potential |
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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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A capacitance is formed by connecting two metallic balls of radius \(r\) by a conducting wire, and two oppositely charged identical metallic hemispheres \((A,B)\) slightly larger than the balls. The separation between the hemispheres and the respective balls is \(d.\) The capacitance between \(A,B\) is:
| 1. | \(\dfrac{4\pi\varepsilon_0r^2}{d}\) | 2. | \(\dfrac{2\pi\varepsilon_0r^2}{d}\) |
| 3. | \(\dfrac{\pi\varepsilon_0r^2}{d}\) | 4. | \(\dfrac{\pi\varepsilon_0r^2}{2d}\) |
Subtopic: Capacitance |
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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. \(4W_1 = W_2\)
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 uniformly charged thin rod of length \(L\) carries a total charge \(q.\) The potential at a point \(A,\) on the perpendicular bisector of the rod, and at a distance \(L\) from its centre is:
\(\left(\text{take}~ k=\dfrac{1}{4\pi\varepsilon_0}\right) \)
\(\left(\text{take}~ k=\dfrac{1}{4\pi\varepsilon_0}\right) \)
| 1. | \(\dfrac{kq}{L}\) | 2. | less than \(\dfrac{kq}{L}\) |
| 3. | greater than \(\dfrac{kq}{L}\) | 4. | zero |
Subtopic: Electric Potential |
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A charge is uniformly distributed on the circumference of a disc, and the potential at its centre is \(5\) volt. If the charge was uniformly distributed on the surface of this disc, the potential at a point \(P\) on its axis, at a distance equal to the disc's radius from its centre, equals:
1. \(10\) V
2. \(5 \sqrt 2\) V
3. \(10 \sqrt 2\) V
4. \(10 (\sqrt {2} -1)\) V
1. \(10\) V
2. \(5 \sqrt 2\) V
3. \(10 \sqrt 2\) V
4. \(10 (\sqrt {2} -1)\) V
Subtopic: Electric 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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A particle \((P)\) of mass \(m\) is placed on the axis of a uniform circular ring of radius \(R\) and mass \(M.\) Its distance \((OP)\) from the centre \((O)\) of the ring is equal to \(R.\) Let the net gravitational field at the centre of the ring be \(g.\) Then, the gravitational potential energy of the interaction of the system is:
1. \(-MgR\)
2. \(-mgR\)
3. \(\dfrac{-MgR}{\sqrt2}\)
4. \(\dfrac{-mgR}{\sqrt2}\)
1. \(-MgR\)
2. \(-mgR\)
3. \(\dfrac{-MgR}{\sqrt2}\)
4. \(\dfrac{-mgR}{\sqrt2}\)
Subtopic: Electric Potential Energy |
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