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Q. No.

Two identical rectangular plane sheet \(A\) and \(B\) each of surface charge density \(\varepsilon_0 \text{Cm}^{-2}\) are placed parallel to each other as shown in figure. The electric field at the mid point \(P\) will be: 

  
1. \(2 ~\text{NC}^{-1}\)
2. \(1~\text{NC}^{-1}\)
3. \(0.5~\text{NC}^{-1}\)
4. zero
Q1:
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Subtopic:  Electric Field |
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Match List-I with List-II: 
List-I
(Application of Gauss Law)		 List-II
(Value of \(|E|\))
A Field inside thin shell I \( \frac{\lambda}{2 \pi \varepsilon_0 r} \hat{n} \)
B Field outside thin shell II \( \frac{q}{4 \pi \varepsilon_0 R^2} \hat{r} \)
C Field of thin shell at the surface III \( \frac{q}{4 \pi \varepsilon_0 r^2} \hat{r}\)
D Field due to long charged wire  IV zero
(Here symbols have their usual meaning and \(R\) is the radius of the thin shell) 
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

 
Q2:
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Subtopic:  Gauss's Law |
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A particle of mass \(m\) and charge \(q\) is placed in a uniform electric field \(E\) at \(t=0~\text s.\) The kinetic energy of the particle after time \(t\) is:
1. \(\large\frac{Eqm}{t}\)
2. \(\large\frac{E^2q^2t^2}{2m}\)
3. \(\large\frac{2E^2t^2}{qm}\)
4. \(\large\frac{Eq^2m}{2t^2}\)
Q3:
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Subtopic:  Electric Field |
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If \(\oint_s \vec{E} \cdot \overrightarrow{d S}=0\) over a surface, then:
 
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.
Q4:
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Subtopic:  Gauss's Law |
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An electric dipole is placed at an angle of \(30^\circ\) with an electric field of intensity \(2\times 10^5 ~\text{NC}^{-1}\). It experiences a torque equal to \(4~\text{N-m}\). Calculate the magnitude of charge on the dipole if the dipole length is \(2~\text{cm}\).
1. \(2~\text{mC}\) 2. \(8~\text{mC}\)
3. \(6~\text{mC}\) 4. \(4~\text{mC}\)
Q5:
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Subtopic:  Electric Dipole |
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According to Gauss law of electrostatics, 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
Q6:
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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. \(\frac{Q}{\varepsilon_0}\times10^{-6}\) 2. \(\frac{2Q}{3\varepsilon_0}\times10^{-3}\)
3. \(\frac{Q}{6\varepsilon_0}\times10^{-3}\) 4. \(\frac{Q}{6\varepsilon_0}\times10^{-6} \)
Q7:
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Subtopic:  Gauss's Law |
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Two point charges \({-q}\) and \({+q}\) are placed at a distance of \({L},\) as shown in the figure.
        
The magnitude of electric field intensity at a distance \({R}~({R}>>{L})\) varies as:
1. \(\frac{1}{{R}^{6}}\) 2. \(\frac{1}{{R}^{2}}\)
3. \(\frac{1}{{R}^{3}}\) 4. \(\frac{1}{{R}^{4}}\)
Q8:
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Subtopic:  Electric Dipole |
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Twelve point charges each of charge \(q\) C are placed at the circumference of a circle of radius \(r\) m with equal angular spacing. If one of the charges is removed, the net electric field (in N/C) at the centre of the circle is:
(\(\varepsilon_0 \)-permittivity of free space)
1. \(\frac{13q}{4\pi \varepsilon_0r^2}\)
2. zero
3. \(\frac{q}{4\pi \varepsilon_0r^2}\)
4. \(\frac{12q}{4\pi \varepsilon_0r^2}\)

Q9:
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Subtopic:  Electric Field |
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The ratio of coulomb's electrostatic force to the gravitational force between an electron and a proton separated by some distance is \(2.4\times 10^{39}\). The ratio of the proportionality constant, \(K=\frac{1}{4\pi\varepsilon_0}\) to the gravitational constant \(G\) is nearly:
(Given that the charge of the proton and electron each \(=1.6\times 10^{-19}\), the mass of the electron = \(9.11\times 10^{-31}\) kg, the mass of the proton \(=1.67\times 10^{-27}\) kg):
1. \(10^{20}\) 2. \(10^{30}\)
3. \(10^{40}\) 4. \(10\)
Q10:
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Subtopic:  Coulomb's Law |
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