Q. No.| List-I (Application of Gauss Law) |
List-II (Value of \(|E|\)) |
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| A. | The field inside a thin shell | I. | \( \dfrac{\lambda}{2 \pi \varepsilon_0 r} \hat{n} \) |
| B. | The field outside a thin shell | II. | \( \dfrac{q}{4 \pi \varepsilon_0 R^2} \hat{r} \) |
| C. | The field of thin shell at the surface | III. | \( \dfrac{q}{4 \pi \varepsilon_0 r^2} \hat{r}\) |
| D. | The field due to a long charged wire | IV. | zero |
Choose the correct answer from the options given below:
| 1. | A-IV, B-III, C-I, D-II |
| 2. | A-I, B-II, C-III, D-IV |
| 3. | A-IV, B-III, C-II, D-I |
| 4. | A-I, B-III, C-II, D-IV |
| 1. | the electric field inside the surface is necessarily uniform. |
| 2. | the number of flux lines entering the surface must be equal to the number of flux lines leaving it. |
| 3. | the magnitude of electric field on the surface is constant. |
| 4. | all the charges must necessarily be inside the surface. |
According to Gauss's law in electrostatics, the electric flux through a closed surface depends on:
| 1. | the area of the surface |
| 2. | the quantity of charges enclosed by the surface |
| 3. | the shape of the surface |
| 4. | the volume enclosed by the surface |
| 1. | \(\dfrac{Q}{\varepsilon_0}\times10^{-6}\) | 2. | \(\dfrac{2Q}{3\varepsilon_0}\times10^{-3}\) |
| 3. | \(\dfrac{Q}{6\varepsilon_0}\times10^{-3}\) | 4. | \(\dfrac{Q}{6\varepsilon_0}\times10^{-6} \) |
Two parallel infinite line charges with linear charge densities \(+\lambda~\text{C/m}\) and \(+\lambda~\text{C/m}\) are placed at a distance \({R}.\) The electric field mid-way between the two line charges is:
| 1. | \(\frac{\lambda}{2 \pi \varepsilon_0 {R}}~\text{N/C}\) | 2. | zero |
| 3. | \(\frac{2\lambda}{ \pi \varepsilon_0 {R}} ~\text{N/C}\) | 4. | \(\frac{\lambda}{ \pi \varepsilon_0 {R}}~\text{N/C}\) |
A sphere encloses an electric dipole with charges \(\pm3\times10^{-6}~\text C.\) What is the total electric flux through the sphere?
1. \(-3\times10^{-6}~\text{N-m}^2/\text C\)
2. zero
3. \(3\times10^{-6}~\text{N-m}^2/\text C\)
4. \(6\times10^{-6}~\text{N-m}^2/\text C\)
The electric field in a certain region is acting radially outward and is given by \(E=Aa.\) A charge contained in a sphere of radius \(a\) centered at the origin of the field will be given by:
| 1. | \(4 \pi \varepsilon_{{o}} {A}{a}^2\) | 2. | \(\varepsilon_{{o}} {A} {a}^2\) |
| 3. | \(4 \pi \varepsilon_{{o}} {A} {a}^3\) | 4. | \(\varepsilon_{{o}} {A}{a}^3\) |
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. \(\dfrac{q}{2\varepsilon_0}\)
| 1. | be reduced to half |
| 2. | remain the same |
| 3. | be doubled |
| 4. | increase four times |
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
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