Q. No.The point charges \(8~\mu\text{C}\) and \(-2~\mu\text{C}\) are located at \(x =2~\text{cm}\) and \(x =4~\text{cm},\) respectively on the \(x\)-axis. The ratio of electric flux due to these through two spheres of radii \(3~\text{cm}\) and \(5~\text{cm}\) with their centres at the origin is:
1. \(4:1\)
2. \(3:4\)
3. \(4:3\)
4. \(4:5\)
1. \(4:1\)
2. \(3:4\)
3. \(4:3\)
4. \(4:5\)
Subtopic: Gauss's Law |
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A thin ring of radius \(35~\text{cm}\) is uniformly charged with a total charge of \(Q\) coulomb. If the magnitude of the electric field at centre of the half ring is \(100~\text{V/m},\) then the value of \(Q\) is: (in nC)
\(\left(\varepsilon_{o}=8.85 \times 10^{-12} ~\text{C}^2 / \text{Nm}^2 \text { and } \pi=3.14\right)\)
1. \(2.14\)
2. \(2.44\)
3. \(3.25\)
4. \(0.7\)
\(\left(\varepsilon_{o}=8.85 \times 10^{-12} ~\text{C}^2 / \text{Nm}^2 \text { and } \pi=3.14\right)\)
1. \(2.14\)
2. \(2.44\)
3. \(3.25\)
4. \(0.7\)
Subtopic: Gauss's Law |
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Two point charges \(2q\) and \(q\) are placed at vertex \(A\) and centre of face \(CDEF\) of the cube as shown in figure. The electric flux passing through the cube is:
1. \(\dfrac{3 q}{\varepsilon_0}\)
2. \(\dfrac{{q}}{\varepsilon_0}\)
3. \(\dfrac{3 q}{2 \varepsilon_0}\)
4. \(\dfrac{3 q}{4 \varepsilon_0}\)
1. \(\dfrac{3 q}{\varepsilon_0}\)
2. \(\dfrac{{q}}{\varepsilon_0}\)
3. \(\dfrac{3 q}{2 \varepsilon_0}\)
4. \(\dfrac{3 q}{4 \varepsilon_0}\)
Subtopic: Gauss's Law |
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An infinitely long wire has uniform linear charge density \(\lambda=2 ~\text{nC/m}.\) The net flux through a Gaussian cube of side length \(\sqrt{3}~ \text{cm} , \) if the wire passes through any two corners of the cube, that are maximally displaced from each other, would be \(x~ \text{Nm}^2 \text{C}^{-1} ,\) where \(x \) is:
[Neglect any edge effects and use \(1 /\left(4 \pi \varepsilon_0\right)=9 \times 10^9 ~\text{SI} \) units]
1. \(0.72~\pi \)
2. \(1.44~\pi \)
3. \(6.48~\pi \)
4. \(2.16~\pi \)
[Neglect any edge effects and use \(1 /\left(4 \pi \varepsilon_0\right)=9 \times 10^9 ~\text{SI} \) units]
1. \(0.72~\pi \)
2. \(1.44~\pi \)
3. \(6.48~\pi \)
4. \(2.16~\pi \)
Subtopic: Gauss's Law |
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The electric field in a region is given by \(\vec{E} = (2\hat i+ 4\hat j + 6\hat k ) × 10^3 ~\text{N/C}.\) The flux of the field through a rectangular surface parallel to \(xz\text-\)plane is \(6.0~\text{Nm}^2\text C^{-1} .\) The area of the surface is: (in \(\text{cm}^2\))
1. \(16\)
2. \(15\)
3. \(17\)
4. \(14\)
1. \(16\)
2. \(15\)
3. \(17\)
4. \(14\)
Subtopic: Gauss's Law |
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A point charge causes an electric flux of \(-2 \times 10^4 ~{\text {Nm}}^2 {\text C}^{-1}\) to pass through a spherical Gaussian surface of \(8.0~\text{cm}\) radius, centred on the charge. The value of the point charge is: (Given: \(\varepsilon_0=8.85 \times 10^{-12} ~\text C^2 \text N^{-1} \text m^{-2}\))
1. \(15.7 \times 10^{-8}~ \text{C} \)
2. \(17.7 \times 10^{-8} ~\text{C} \)
3. \(-15.7 \times 10^{-8}~ \text{C} \)
4. \(-17.7 \times 10^{-8}~ \text{C} \)
1. \(15.7 \times 10^{-8}~ \text{C} \)
2. \(17.7 \times 10^{-8} ~\text{C} \)
3. \(-15.7 \times 10^{-8}~ \text{C} \)
4. \(-17.7 \times 10^{-8}~ \text{C} \)
Subtopic: Gauss's Law |
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The electric flux is \(\phi=\alpha \sigma+\beta \lambda\) where \(\lambda\) are \(\sigma\) are linear and surface charge density, respectively. \(\left(\dfrac{\alpha}{\beta}\right)\) represents
1. electric field
2. area
3. charge
4. displacement
1. electric field
2. area
3. charge
4. displacement
Subtopic: Gauss's Law |
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Match List-I with List-II.
Choose the correct answer from the options given below:
| List-I | List-II | ||
| \(\mathrm{A.}\) | Electric field inside (distance |
\(\mathrm{I.}\) | \(\dfrac{\sigma}{\varepsilon_0}\) |
| \(\mathrm{B.}\) | Electric field at distance \(r>0\) |
\(\mathrm{II.}\) | \(\dfrac{\sigma}{2\varepsilon_0}\) |
| \(\mathrm{C.}\) | Electric field outside (distance |
\(\mathrm{III.}\) | \(0\) |
| \(\mathrm{D.}\) | Electric field between \(2\) oppositely charged infinite plane parallel sheets with uniform surface charge density \(\sigma.\) |
\(\mathrm{IV.}\) | \(\dfrac{\sigma R^2}{\varepsilon_0 r^2}\) |
| 1. | \(\mathrm{A\text-II,B\text-I, C\text-IV,D\text-III}\) |
| 2. | \(\mathrm{A\text-III,B\text-II, C\text-IV,D\text-I}\) |
| 3. | \(\mathrm{A\text-IV,B\text-II, C\text-III,D\text-I}\) |
| 4. | \(\mathrm{A\text-IV,B\text-I, C\text-III,D\text-II}\) |
Subtopic: Gauss's Law |
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A line charge of length \(a/2\) is kept at the center of an edge \(\text {BC}\) of a cube \(\text {ABCDEFGH}\) having edge length a as shown in the figure. If the density of line charge is \(\lambda C\) per unit length, then the total electric flux through all the faces of the cube will be _____ (Take,\(\epsilon_0\) as the free space permittivity)
1. \(\dfrac{\lambda a}{4 \epsilon_0} \)
2. \(\dfrac{\lambda a}{2 \epsilon_0} \)
3. \(\dfrac{\lambda a}{16 \epsilon_0}\)
4. \(\dfrac{\lambda a}{8 \epsilon_0}\)
1. \(\dfrac{\lambda a}{4 \epsilon_0} \)
2. \(\dfrac{\lambda a}{2 \epsilon_0} \)
3. \(\dfrac{\lambda a}{16 \epsilon_0}\)
4. \(\dfrac{\lambda a}{8 \epsilon_0}\)
Subtopic: Gauss's Law |
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An electric field, \(\overrightarrow{{E}}=\frac{2 \hat{i}+6 \hat{{j}}+8 \hat{{k}}}{\sqrt{6}}\) passes through the surface of \(4 \mathrm{~m}^2\) area having unit vector \(\hat{n}=\left(\frac{2 \hat{i}+\hat{j}+\hat{k}}{\sqrt{6}}\right).\) The electric flux for that surface is:
1. \(32~\text{Vm}\)
2. \(12~\text{Vm}\)
3. \(16~\text{Vm}\)
4. \(24~\text{Vm}\)
1. \(32~\text{Vm}\)
2. \(12~\text{Vm}\)
3. \(16~\text{Vm}\)
4. \(24~\text{Vm}\)
Subtopic: Gauss's Law |
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