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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 |
Level 4: Below 35%

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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 |
Level 3: 35%-60%

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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 |
Level 3: 35%-60%

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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
Subtopic:  Relation between Field & Potential |
Level 4: Below 35%

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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 |
Level 4: Below 35%

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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 |
Level 4: Below 35%

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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:
\(\left(\text{take}~ k=\dfrac{1}{4\pi\varepsilon_0}\right) \)
1. \(\dfrac{kq}{L}\) 2. less than \(\dfrac{kq}{L}\)
3. greater than \(\dfrac{kq}{L}\) 4. zero
Subtopic:  Electric Potential |
Level 3: 35%-60%

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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
Subtopic:  Electric Potential |
Level 3: 35%-60%

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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
Subtopic:  Capacitance |
Level 3: 35%-60%

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The left plate \(A\) of an air capacitor is connected to the positive terminal while the right plate \(B\) is connected to the negative terminal of a cell of voltage \(V_0.\) Assume that the plate area is \(A,\) and the plate separation is \(d.\) If a slab of dielectric constant \(K\) is inserted into the space between the plates, the electric field in the dielectric will be: (compared to the air capacitor)
                      
 
1. more.
2. less.
3. equal.
4. more or less or equal depending on the value of \(K\).
Subtopic:  Dielectrics in Capacitors |
Level 3: 35%-60%

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