Q. No.A uniform electric field \(\vec E=(a\widehat i+b\widehat j),\) intersects a surface of area \(A.\) What is the flux through this area if the surface lies in \(x\text-z\) plane?
| 1. | zero | 2. | \(aA\) |
| 3. | \(bA\) | 4. | \(A\sqrt{a^2+b^2}\) |
Subtopic: Gauss's Law |
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If \(\vec E=\dfrac{E_0x}{a}(\widehat i),\) then electric flux through the cube of side \(a,\) as shown in the figure, will be:
(where \(x\) is in metre)
1. zero
2. \(E_0a^2\)
3. \(E_0a^3\)
4. \(E_0a\)
(where \(x\) is in metre)
1. zero
2. \(E_0a^2\)
3. \(E_0a^3\)
4. \(E_0a\)
Subtopic: Gauss's Law |
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What is the flux of electric field \(\vec E = 3\times 10^3 \hat i~ \text{N/C}\) through a square of \(10\) cm on a side whose plane is parallel to the \(yz\text-\)plane?
| 1. | \(15~\text{Nm}^{2}/\text{C}\) | 2. | \(10~\text{Nm}^{2}/\text{C}\) |
| 3. | \(30~\text{Nm}^{2}/\text{C}\) | 4. | \(0\) |
Subtopic: Gauss's Law |
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Consider a region inside where there are various types of charges but the total charge is zero. At points outside the region:
| (a) | the electric field is necessarily zero. |
| (b) | the electric field is due to the dipole moment of the charge distribution only. |
| (c) | the dominant electric field is \(\propto \dfrac 1 {r^3}\), for large \(r\), where \(r\) is the distance from the origin in this region. |
| (d) | the work done to move a charged particle along a closed path, away from the region, will be zero. |
Which of the above statements are true?
1. (b) and (d)
2. (a) and (c)
3. (b) and (c)
4. (c) and (d)
Subtopic: Gauss's Law |
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A spherical conducting shell of inner radius \(r_1\) and outer radius \(r_2\) has a charge \(Q\). A charge \(q\) is placed at the centre of the shell. The surface charge density on the outer surfaces of the shell is:
| 1. | \(\dfrac{Q+q}{4 \pi r_{2}^{2}}\) | 2. | \(\dfrac{q}{4 \pi r_{1}^{2}}\) |
| 3. | \(\dfrac{-Q+q}{4 \pi r_{2}^{2}}\) | 4. | \(\dfrac{-q}{4 \pi r_{1}^{2}}\) |
Subtopic: Gauss's Law |
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A sphere encloses an electric dipole with charges \(\pm 3\times 10^{-6}~\text{C}\). What is the total electric flux through the sphere?
1. \(-3\times 10^{-6}~\text{Nm}^2/\text{C}\)
2. zero
3. \(3\times 10^{-6}~\text{Nm}^2/\text{C}\)
4. \(6\times 10^{-6}~\text{Nm}^2/\text{C}\)
1. \(-3\times 10^{-6}~\text{Nm}^2/\text{C}\)
2. zero
3. \(3\times 10^{-6}~\text{Nm}^2/\text{C}\)
4. \(6\times 10^{-6}~\text{Nm}^2/\text{C}\)
Subtopic: Gauss's Law |
92%
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A point charge causes an electric flux of \(-1.0\times 10^{3}~\text{Nm}^2/\text{C}\) to pass through a spherical Gaussian surface of \(10.0\) cm radius centered on the charge. If the radius of the Gaussian surface were doubled, how much flux would pass through the surface?
1. \(- 2.0×10^{3}~\text{Nm}^2/\text{C}\)
2. \(- 1.0 ×10^{3}~\text{Nm}^2/\text{C}\)
3. \(2.0 ×10^{3}~\text{Nm}^2/\text{C}\)
4. \( 0\)
Subtopic: Gauss's Law |
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A charge \(Q~\mu\text{C}\) is placed at the centre of a cube. The flux coming out from any one of its faces will be: (in SI unit)
| 1. | \(\dfrac{Q}{\varepsilon_0}\times10^{-6}\) | 2. | \(\dfrac{2Q}{3\varepsilon_0}\times10^{-3}\) |
| 3. | \(\dfrac{Q}{6\varepsilon_0}\times10^{-3}\) | 4. | \(\dfrac{Q}{6\varepsilon_0}\times10^{-6} \) |
Subtopic: Gauss's Law |
75%
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Given below are two statements:
| Assertion (A): | The number of field lines drawn from a charge is proportional to the magnitude of the charge. |
| Reason (R): | The electric field at any point is proportional to the magnitude of the source charge. |
| 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. |
Subtopic: Gauss's Law |
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An electric dipole is enclosed by a Gaussian surface (see figure). The total electric flux through the surface is:
1. \(q / \varepsilon_0\)
2. zero
3. \(-q / \varepsilon_0\)
4. \(2q / \varepsilon_0\)
1. \(q / \varepsilon_0\)
2. zero
3. \(-q / \varepsilon_0\)
4. \(2q / \varepsilon_0\)
Subtopic: Gauss's Law |
87%
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