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Q. No.A dipole (\(p\)) is placed so that it is always aligned along the x-axis but it can undergo displacement along the x-axis. The dipole is placed exactly midway between two fixed charges \(-Q\) and \(Q,\) in two possible ways.
Then, the dipole is:
1.
stable in both \(A,B\)
2.
stable in \(A\), unstable in \(B\)
3.
unstable in \(A\), stable in \(B\)
4.
unstable in both \(A,B\)
Subtopic: Energy of Dipole in an External Field |
58%
Level 3: 35%-60%
Hints
A charge '\(q\)' is uniformly distributed within a spherical volume of radius \(R\). A negative point charge \(q'\) is placed at the centre of this sphere so that the electric field of the overall distribution (i.e. \(q\) and \(q'\) together) – vanishes at the mid-point of the radius of the sphere.
If the potential at the surface of the sphere with '\(q\) alone' is \(V_1\) and with \(q\), \(q'\) together is \(V_2\), then:
1. \(\dfrac{V_1}{V_2}=\dfrac{2}{1}\)
2. \(\dfrac{V_1}{V_2}=\dfrac{4}{3}\)
3. \(\dfrac{V_1}{V_2}=\dfrac{4}{1}\)
4. \(\dfrac{V_1}{V_2}=\dfrac{8}{7}\)
If the potential at the surface of the sphere with '\(q\) alone' is \(V_1\) and with \(q\), \(q'\) together is \(V_2\), then:
1. \(\dfrac{V_1}{V_2}=\dfrac{2}{1}\)
2. \(\dfrac{V_1}{V_2}=\dfrac{4}{3}\)
3. \(\dfrac{V_1}{V_2}=\dfrac{4}{1}\)
4. \(\dfrac{V_1}{V_2}=\dfrac{8}{7}\)
Subtopic: Electric Potential |
Level 3: 35%-60%
Hints
Three concentric spherical conducting shells of radii \(a,b,\) and \(c~(a<b<c)\) are placed as shown. Let \(C_{ab}\) be the capacitance when \(a\) and \(b\) spheres are charged with \(+Q,-Q\) and similarly, let \(C_{bc}\) be the capacitance between \(b\) and \(c\) spheres while \(C_{ac}\) be the capacitance between \(a\) and \(c\) sphere. Then:
1. \(C_{ab}+C_{bc}=C_{ac}\)
2. \(\dfrac{1}{C_{ab}}+\dfrac{1}{C_{bc}}=\dfrac{1}{C_{ac}}\)
3. \(\sqrt{C_{ab}\cdot C_{bc}}=C_{ac}\)
4. \(C_{ab}-C_{bc}=C_{ac}\)
1. \(C_{ab}+C_{bc}=C_{ac}\)
2. \(\dfrac{1}{C_{ab}}+\dfrac{1}{C_{bc}}=\dfrac{1}{C_{ac}}\)
3. \(\sqrt{C_{ab}\cdot C_{bc}}=C_{ac}\)
4. \(C_{ab}-C_{bc}=C_{ac}\)
Subtopic: Capacitance |
62%
Level 2: 60%+
Hints
Two metallic plates are placed parallel to each other, at a separation \(d.\) A dielectric (\(K=2\)) of width \(d/3\) is inserted into space between the plates, parallel to plates: the separation between the plates being \(d.\) The capacitance of the plates:
1. increases by \(20\)%
2. decreases by \(20\)%
3. increases by \(33\)%
4. decreases by \(25\)%
1. increases by \(20\)%
2. decreases by \(20\)%
3. increases by \(33\)%
4. decreases by \(25\)%
Subtopic: Dielectrics in Capacitors |
73%
Level 2: 60%+
Hints
A metallic sphere of radius \(R\) is given a charge \(Q.\) The energy stored in the sphere due to this charge is:
| 1. | \(\dfrac{Q^2}{4\pi\varepsilon_0R}\) | 2. | \(\dfrac{2Q^2}{4\pi\varepsilon_0R}\) |
| 3. | \(\dfrac12 \left ( \dfrac{Q^2}{4\pi\varepsilon_0R} \right )\) | 4. | \(\dfrac{Q^2}{16\pi\varepsilon_0R}\) |
Subtopic: Energy stored in Capacitor |
70%
Level 2: 60%+
Hints
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%
Hints
A dielectric slab is inserted between the plates of an isolated charged capacitor. Which of the following remains unchanged?
Choose the correct option from given ones:
| (I) | The charge on the plates. |
| (II) | The potential difference between the plates. |
| (III) | The energy stored in the capacitor. |
Choose the correct option from given ones:
| 1. | (I) only | 2. | (I) and (II) |
| 3. | (I) and (III) | 4. | (I), (II) and (III) |
Subtopic: Dielectrics in Capacitors |
72%
Level 2: 60%+
Hints
A capacitor is constructed by taking metallic circular discs of radius \(r\) placed face-to-face with a separation of \(d.\) A dielectric slab is inserted into the space between the plates so that it fills the entire width, but only half the area between the plates. The dielectric constant is \(K.\) Then, the capacitance is:
| 1. | \(\dfrac{K\varepsilon_0\pi r^2}{d}\) | 2. | \(\dfrac{K\varepsilon_0\pi r^2}{2d}\) |
| 3. | \(\dfrac{K+1}{2}\dfrac{\varepsilon_0\pi r^2}{d}\) | 4. | None of the above |
Subtopic: Dielectrics in Capacitors |
60%
Level 2: 60%+
Hints
A parallel plate capacitor \((C)\) is charged by connecting it to a battery (EMF \(E\)). A dielectric slab is inserted into the space between the plates.
Choose the correct answer from the options given below:
| (I) | The charge on the plates increases. |
| (II) | The energy stored in the capacitor increases. |
| (III) | Work is done by the battery as the slab is inserted. |
Choose the correct answer from the options given below:
| 1. | (I), and (II) are True. |
| 2. | (I) and (III) are True. |
| 3. | only (I) is True. |
| 4. | (I), (II), and (III) are True. |
Subtopic: Capacitance |
65%
Level 2: 60%+
Hints
An uncharged capacitor \((C)\) is connected to a battery of emf \(E\). Once it is fully charged, it is connected to a second battery of emf \(2E\). The positive terminal of the capacitor and battery are connected and their negative terminals are similarly connected together. The energy dissipated as heat, when the second battery is connected is:
| 1. | \(\dfrac{3}{2}CE^2\) | 2. | \(\dfrac{1}{2}CE^2\) |
| 3. | \(CE^2\) | 4. | \(\dfrac{5}{2}CE^2\) |
Subtopic: Energy stored in Capacitor |
53%
Level 3: 35%-60%
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