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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The region between two concentric spheres of radii '\(a\)' and '\(b\)' , respectively (see figure), has volume charge density \(\rho=\frac{A}{r}\), where \(A\) is a constant and \(r\) is the distance from the centre. At the centre of the spheres is a point charge \(Q\). The value of \(A\) such that the electric field in the region between the spheres will be constant, is:
1. \( \frac{Q}{2 \pi a^2} \)
2. \(\frac{Q}{2 \pi\left(b^2-a^2\right)} \)
3. \(\frac{2 Q}{\pi\left(a^2-b^2\right)} \)
4. \(\frac{2 Q}{\pi a^2}\)
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Consider that four closed surfaces, \(S_1,S_2,S_3,\) and \(S_4\) enclosing different charge distributions as shown in the figure.
What is the correct relationship between their respective electric fluxes \(\phi_1,\phi_2,\phi_3,\) and \(\phi_4\text{?}\)
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| 1. | \(\phi_1=\phi_2=\phi_3=\phi_4 \) | 2. | \(\phi_1>\phi_3;~\phi_2<\phi_4 \) |
| 3. | \(\phi_1>\phi_2>\phi_3>\phi_4 \) | 4. | \(\phi_1<\phi_2=\phi_3>\phi_4 \) |
Subtopic: Gauss's Law |
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A charge \(Q\) is placed at a distance \(\dfrac{a}{2}\) above the centre of the square surface of the edge \(a\) as shown in the figure. The electric flux through the square surface is:
2. \(\dfrac{Q}{2{\epsilon_0}}\)
3. \(\dfrac{Q}{3{\epsilon_0}}\)
4. \(\dfrac{Q}{{\epsilon_0}}\)
2. \(\dfrac{Q}{2{\epsilon_0}}\)
3. \(\dfrac{Q}{3{\epsilon_0}}\)
4. \(\dfrac{Q}{{\epsilon_0}}\)
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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. \(2.16~\pi \)
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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. \(14\)
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A point charge of \(+12~\mathrm{\mu C}\) is at a distance \(6\) cm vertically above the centre of a square of side \(12\) cm as shown in figure. The magnitude of the electric flux through the square will be:
1. \( 226 \times 10^2 ~\frac{\mathrm{Nm}^2}{\mathrm{C}}\)
2. \( 226 \times 10^3 ~\frac{\mathrm{Nm}^2}{\mathrm{C}}\)
3. \(326 \times 10^3 ~\frac{\mathrm{Nm}^2}{\mathrm{C}}\)
4. \( 326 \times 10^2 ~\frac{\mathrm{Nm}^2}{\mathrm{C}}\)
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. \(-17.7 \times 10^{-8}~ \text{C} \)
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