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Q. No.The ratio of the electric flux linked with shell \(A\) and shell \(B\) in the diagram shown below is:
| 1. | \(1: 1\) | 2. | \(1: 2\) |
| 3. | \(1: 4\) | 4. | \(4: 2\) |
| 1. | be reduced to half |
| 2. | remain the same |
| 3. | be doubled |
| 4. | increase four times |
What is the flux through a cube of side \(a,\) if a point charge of \(q\) is placed at one of its corners?
1. \(\dfrac{2q}{\varepsilon_0}\)
2. \(\dfrac{q}{8\varepsilon_0}\)
3. \(\dfrac{q}{\varepsilon_0}\)
4. \(\dfrac{q}{2\varepsilon_0}\)
A hollow metal sphere of radius \(R\) is uniformly charged. The electric field due to the sphere at a distance \(r\) from the centre:
| 1. | decreases as \(r\) increases for \(r<R\) and for \(r>R\). |
| 2. | increases as \(r\) increases for \(r<R\) and for \(r>R\). |
| 3. | is zero as \(r\) increases for \(r<R\), decreases as \(r\) increases for \(r>R\). |
| 4. | is zero as \(r\) increases for \(r<R\), increases as \(r\) increases for \(r>R\). |
Which of the following graphs shows the variation of electric field \(E\) due to a hollow spherical conductor of radius \(R\) as a function of distance from the centre of the sphere?
| 1. |  |
2. |  |
| 3. |  |
4. |  |
A square surface of a side \(L\) \(\text{(m)}\) is in the plane of the paper. A uniform electric field \(\vec{E}\) \(\text{(V/m)},\) also in the plane of the paper, is limited only to the lower half of the square surface, (see figure). The electric flux in SI units associated with the surface is:
| 1. | \(EL^2/ ( 2ε_0 )\) | 2. | \(EL^2 / 2\) |
| 3. | zero | 4. | \(EL^2\) |
A hollow cylinder has a charge \(q\) coulomb within it (at the geometrical centre). If \(\phi\) is the electric flux in units of Volt-meter associated with the curved surface \(B,\) the flux linked with the plane surface \(A\) in units of volt-meter will be:
1. \(\frac{1}{2}\left(\frac{q}{\varepsilon_0}-\phi\right)\)
2. \(\frac{q}{2\varepsilon_0}\)
3. \(\frac{\phi}{3}\)
4. \(\frac{q}{\varepsilon_0}-\phi\)
A point charge \(q\) is placed at the center of the open face of a hemispherical surface as shown in the figure. The flux linked with the surface is:
1. zero
2. \(\frac{q}{2\varepsilon_0}\)
3. \(\frac{q}{\varepsilon_0}\)
4. \(q \pi r^2\)
Refer to the arrangement of charges in the figure and a Gaussian surface of a radius \(R\) with \(Q\) at the centre. Then:
| (a) | total flux through the surface of the sphere is \(\frac{-Q}{\varepsilon_0}.\) |
| (b) | field on the surface of the sphere is \(\frac{-Q}{4\pi \varepsilon_0 R^2}.\) |
| (c) | flux through the surface of the sphere due to \(5Q\) is zero. |
| (d) | field on the surface of the sphere due to \(-2Q\) is the same everywhere. |
Choose the correct statement(s):
| 1. | (a) and (d) | 2. | (a) and (c) |
| 3. | (b) and (d) | 4. | (c) and (d) |
| (a) | \(\oint_s {E} . {dS} \neq 0\) on any surface |
| (b) | \(\oint_s {E} . {dS} = 0\) if the charge is outside the surface. |
| (c) | \(\oint_s {E} . {dS}\) could not be defined. |
| (d) | \(\oint_s {E} . {dS}=\frac{q}{\epsilon_0}\) if charges of magnitude \(q\) were inside the surface. |
| 1. | (a) and (d) | 2. | (a) and (c) |
| 3. | (b) and (d) | 4. | (c) and (d) |
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