Q. No.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 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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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 |
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Three charges are placed at the three corners of an equilateral triangle as shown in the figure. The potential at the mid-point of a side with opposite charges is \(2~\text V.\) The potential at the centre of the triangle is:
| 1. | \(2~\text V\) | 2. | \(3~\text V\) |
| 3. | \(2\sqrt3~\text V\) | 4. | \(\dfrac{2}{\sqrt3}~\text V\) |
Subtopic: Electric Potential |
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A non-conducting circular plate is uniformly charged and the potential at its center is \(V_0.\) If all the charge is collected and kept at its edge, then the potential will be:
| 1. | \(2V_0\) | 2. | \(\dfrac{V_0}{2}\) |
| 3. | \(\dfrac{V_0}{3}\) | 4. | \(\dfrac{V_0}{\sqrt2}\) |
Subtopic: Electric Potential |
53%
From NCERT
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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 |
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A metallic sphere \((A)\) is charged to a potential of \(12~\text V\) and then placed in contact with an identical uncharged metallic sphere \((B);\) the two spheres are separated. The process is repeated: the first sphere \((A)\) is again charged to \(12~\text V\) and placed in contact with sphere \(B.\) The final potential of \(B\) is (after it is separated):
1. \(6~\text V\)
2. \(12~\text V\)
3. \(9~\text V\)
4. \(18~\text V\)
1. \(6~\text V\)
2. \(12~\text V\)
3. \(9~\text V\)
4. \(18~\text V\)
Subtopic: Electric Potential |
58%
From NCERT
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Two hemispheres, one of radius \(R\) and the other of radius \(2R\) carry charges \(+Q\) and \(-Q\) respectively, on their surfaces. They are placed so that they share a common centre \(O,\) as shown. The potential at their common centre is: \(\left(k=\dfrac{1}{4\pi\varepsilon_0}\right)\)
| 1. | \(k\dfrac{Q}{R}\) | 2. | \(k\dfrac{Q}{2R}\) |
| 3. | \(-k\dfrac{Q}{2R}\) | 4. | zero |
Subtopic: Electric Potential |
60%
From NCERT
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The potential on the surface of a spherical region varies from \(2\) V to \(4\) V from point to point. There are no charges in the interior of the region.
| Assertion (A): | The potential at the centre cannot be \(0\) V. |
| Reason (R): | Potential in the interior of a sphere must always be greater than the potential on the surface. |
| 1. | (A) is True but (R) is False. |
| 2. | (A) is False but (R) is True. |
| 3. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 4. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
Subtopic: Electric Potential |
63%
From NCERT
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