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. | \(4: 2\) |
What is the flux through a cube of side \(a,\) if a point charge of \(q\) is placed at one of its corners?
1. \(\frac{2q}{\varepsilon_0}\)
2. \(\frac{q}{8\varepsilon_0}\)
3. \(\frac{q}{\varepsilon_0}\)
4. \(\frac{q}{2\varepsilon_0}\)
1. be reduced to half
2. remain the same
3. be doubled
4. increase four times
If there were only one type of charge in the universe, then:
| 1. | \(\oint_{s} \vec{E} \cdot d \vec{s} \neq 0\) on any surface. |
| 2. | \(\oint_{s} \vec{E} \cdot d \vec{s}=0\)if the charge is outside the surface. |
| 3. | \(\oint_{s} \vec{E} \cdot d \vec{s}=\frac{q}{\varepsilon_{0}}\) if charges of magnitude q were inside the surface. |
| 4. | both (2) and (3) are correct. |
The electric field at a distance \(\frac{3R}{2}\) from the centre of a charged conducting spherical shell of radius \(R\) is \(E\). The electric field at a distance \(\frac{R}{2}\) from the centre of the sphere is:
1. \(E\)
2. \(\frac{E}{2}\)
3. \(\frac{E}{3}\)
4. zero
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. |  |
| Assertion (A): | A charge q is placed in a cube of side b. The flux associated with the cube is independent of side length. |
| Reason (R): | Gauss's law is independent of the size of the Gaussian surface. |
In the light of the above statements choose the correct answer from the options given below:
| 1. | Both (A) and (R) are true and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are true but (R) is not the correct explanation of (A). |
| 3. | (A) is true but (R) is false. |
| 4. | Both (A) and (R) are false. |
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 \(r>R\). |
A point charge is placed at the center of the spherical Gaussian surface. The electric flux through the surface is changed if the:
| 1. | sphere is replaced by a cube of the same volume. |
| 2. | sphere is replaced by a cube of half volume. |
| 3. | charge is moved off-centre in the original sphere. |
| 4. | charge is moved just outside the original sphere. |
A square surface of side \(L\) (m) is in the plane of the paper. A uniform electric field \(\vec{E}\) (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. | \(EL^2\) |
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