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Q. No.A pair of parallel metallic plates having a surface area \(A\) (each), facing each other, are placed with a small separation \(d\) between them. The two plates \(\mathrm{(I, II)}\) are given different charges and their potentials \(V_{\mathrm I},V_{\mathrm{II}}\) are measured.
If plate \(\mathrm I\) is given a charge \(+Q\) and plate \(\mathrm{II}\) is given \(-Q,\) then \(V_{\mathrm{I}}=\)
1. \({\Large\frac{Qd}{A\varepsilon_0}}\)
2. \({\Large\frac{Qd}{2A\varepsilon_0}}\)
3. \({\Large\frac{2Qd}{A\varepsilon_0}}\)
4. \({\Large\frac{Qd}{4A\varepsilon_0}}\)
Subtopic: Electric Potential |
60%
Level 2: 60%+
Hints
A parallel plate capacitor is charged by giving it a total charge \(Q,\) resulting in an electric field \(E\) between its plates. A small charge \(q\) is placed between the plates of the capacitor. The force on \(q\) is \(F_1\) and the force between the two plates of the capacitor is \(F_2.\) Then:
| 1. | \(F_1=qE,~F_2=QE\) | 2. | \(F_1=2qE,~F_2=QE\) |
| 3. | \(F_1=2qE,~F_2={\Large\frac{QE}{2}}\) | 4. | \(F_1=qE,~F_2={\Large\frac{QE}{2}}\) |
Subtopic: Capacitance |
Level 3: 35%-60%
Hints
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%
Hints
Two large plane metallic plates of surface area \(A\) are placed parallel to each other, and they are charged oppositely with equal charges: \(+Q,-Q.\) The separation between the two plates is \(d,\) which is very small. A small positive charge \(q~(q\ll Q)\) is placed exactly midway between the two plates. The force on \(q\) due to the remaining charges \((\text{i.e.,}+Q,-Q)\) is: \(\Bigg(k={\large\frac{1}{4\pi\varepsilon_0}}\Bigg)\)
| 1. | \(k{\Large\frac{2qQ}{\big(d^2/4\big)}}\) | 2. | \({\Large\frac{qQ}{\varepsilon_0A}}\) |
| 3. | \({\Large\frac{2qQ}{\varepsilon_0A}}\) | 4. | zero |
Subtopic: Capacitance |
Level 3: 35%-60%
Hints
An uncharged conducting sphere (radius: \(R\)) is placed in the field of a point charge \(Q.\) The potential of the point \(A\) on the sphere, nearest to \(Q,\) is: \(\bigg(k={\large\frac{1}{4\pi\varepsilon_0}}\bigg)\)
1. \(\Large\frac{kQ}{R}\)
2. \(\Large\frac{kQ}{d-R}\)
3. \(\Large\frac{kQ}{d-R^2/d}\)
4. \(\Large\frac{kQ}{d}\)
1. \(\Large\frac{kQ}{R}\)
2. \(\Large\frac{kQ}{d-R}\)
3. \(\Large\frac{kQ}{d-R^2/d}\)
4. \(\Large\frac{kQ}{d}\)
Subtopic: Electric Potential |
Level 3: 35%-60%
Hints
A capacitor is charged up to a voltage \(V_0.\) Thereafter, \(50\%\) of the charge is taken from the positive plate and placed on the negative plate, slowly. If the initial energy stored in the capacitor was \(E_0,\) the magnitude of work done during the removal of \(50\%\) of the charge, is:
| 1. | \(\dfrac{E_0}{2}\) | 2. | \(\dfrac{E_0}{4}\) |
| 3. | \(\dfrac{3E_0}{4}\) | 4. | \(\dfrac{3E_0}{8}\) |
Subtopic: Energy stored in Capacitor |
Level 3: 35%-60%
Hints
Two identical thin non-conducting spherical shells of radius \(r\) are charged uniformly with equal and opposite charges \(+Q,-Q\) and placed, so that their surfaces almost touch each other, externally (see figure). The electric fields at their centres are \(\vec E_A,\vec E_B\) while the potentials are \(V_A,V_B\) respectively. Then:
1. \(\vec E_A=\vec E_B,V_A=V_B\)
2. \(\vec E_A=-\vec E_B,V_A=V_B\)
3. \(\vec E_A=\vec E_B,V_A=-V_B\)
4. \(\vec E_A=-\vec E_B,V_A=-V_B\)
1. \(\vec E_A=\vec E_B,V_A=V_B\)
2. \(\vec E_A=-\vec E_B,V_A=V_B\)
3. \(\vec E_A=\vec E_B,V_A=-V_B\)
4. \(\vec E_A=-\vec E_B,V_A=-V_B\)
Subtopic: Electric Potential |
Level 3: 35%-60%
Hints
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
\(\left(\text{take}~ k=\dfrac{1}{4\pi\varepsilon_0}\right) \)
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%
Hints
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%
Hints
Consider an electric field of the form: \(\vec E=K(y\hat i+x\hat j)\)
where \(K\) is a constant, and \(x,y\) are the coordinates.
where \(K\) is a constant, and \(x,y\) are the coordinates.
| Statement I: | If a charged particle is taken along the \(x\)-axis, no work will be done by the electric field. |
| Statement II: | This electric field is conservative in nature i.e. it can be derived from a potential: \(V(x,y)=C-Kxy\) |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |
Subtopic: Relation between Field & Potential |
Level 3: 35%-60%
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