Q. No.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).
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1. \(\dfrac{3\varepsilon_0A}{2d}\)
2. \(\dfrac{4\varepsilon_0A}{3d}\)
3. \(\dfrac{\varepsilon_0A}{3d}\)
4. \(\dfrac{\varepsilon_0A}{2d}\)
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| 1. | \(15~\text{V}\) | 2. | \(30~\text{V}\) |
| 3. | \(60~\text{V}\) | 4. | \(120~\text{V}\) |
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| 1. | \(2~\text V\) | 2. | \(3~\text V\) |
| 3. | \(2\sqrt3~\text V\) | 4. | \(\dfrac{2}{\sqrt3}~\text V\) |
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| 1. | \(4~\mu\)F | 2. | \(2.5~\mu \)F |
| 3. | \(2.4~\mu \)F | 4. | \(1.5~\mu \)F |
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| 1. | \(8~\mu\text F\) | 2. | \(4~\mu\text F\) |
| 3. | \(1~\mu\text F\) | 4. | \(0.5~\mu\text F\) |
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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. |
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| 1. | \(10\) nF | 2. | \(20\) nF |
| 3. | \(40\) nF | 4. | none of the above |
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| 1. | \(1:2:1\) | 2. | \(1:\dfrac12:1\) |
| 3. | \(1:4:1\) | 4. | \(1:\dfrac14:1\) |
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| 1. | \(\dfrac{4\pi\varepsilon_0r^2}{d}\) | 2. | \(\dfrac{2\pi\varepsilon_0r^2}{d}\) |
| 3. | \(\dfrac{\pi\varepsilon_0r^2}{d}\) | 4. | \(\dfrac{\pi\varepsilon_0r^2}{2d}\) |
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