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. \(\frac{\lambda}{ \pi \varepsilon_0 {R}}~\text{N/C}\) 

Subtopic:  Gauss's Law |
 69%
Level 2: 60%+
NEET - 2019
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A square surface of a side \(L\) \(\text{(m)}\) is in the plane of the paper. A uniform electric field \(\vec{E}\) \(\text{(V/m)},\) also in the plane of the paper, is limited only to the lower half of the square surface, (see figure). The electric flux in SI units associated with the surface is:     
  

1. \(EL^2/ ( 2ε_0 )\) 2.  \(EL^2 / 2\)
3. zero 4. \(EL^2\)
Subtopic:  Gauss's Law |
 83%
Level 1: 80%+
AIPMT - 2006
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Two pith balls carrying equal charges are suspended from a common point by strings of equal length, the equilibrium separation between them is \(r\) (as shown in Fig. I). Now, as shown in Fig. II, the strings are rigidly clamped at half the height. The equilibrium separation between the balls now becomes:
1. \(\dfrac{r}{\sqrt[3]{2}}\) 2. \(\dfrac{r}{\sqrt[2]{2}}\)
3. \(\dfrac{2r}{3}\) 4. none of the above
Subtopic:  Coulomb's Law |
 71%
Level 2: 60%+
AIPMT - 2013
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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. \(\varepsilon_{{o}} {A}{a}^3\)
Subtopic:  Gauss's Law |
 70%
Level 2: 60%+
NEET - 2015
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Two identical charged spheres suspended from a common point by two massless strings of lengths \(l,\) are initially at a distance \(d\) \(\left ( d\ll l \right )\) apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity \(v.\) Then, \(v\) varies as a function of the distance \(x\) between the sphere, as:
1. \(v\propto x\)
2. \(v\propto x^{-1/2}\)
3. \(v\propto x^{-1}\)
4. \(v\propto x^{1/2}\)
Subtopic:  Coulomb's Law |
 77%
Level 2: 60%+
NEET - 2016
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An electric dipole is placed at an angle of \(30^\circ\) with an electric field intensity \(2\times10^5~ \text{N/C}\). It experiences a torque equal to \(4~\text{N-m}\). The charge on the dipole, if the dipole length is \(2~ \text{cm}\), is:
1. \(8~\text{mC}\)  2. \(2~\text{mC}\)
3. \(5~\text{mC}\) 4. \(7~\mu \text{C}\)
Subtopic:  Electric Dipole |
 88%
Level 1: 80%+
NEET - 2016
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If a charge \(Q\) is situated at the corner of a cube, the electric flux passing through all six faces of the cube is:

1. \(\frac{Q}{6\varepsilon_0}\) 2. \(\frac{Q}{8\varepsilon_0}\)
3. \(\frac{Q}{\varepsilon_0}\) 4. \(\frac{Q}{2\varepsilon_0}\)

Subtopic:  Gauss's Law |
 70%
Level 2: 60%+
AIPMT - 2000
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If \(10^9\) electrons move out of a body to another body every second, how much time approximately is required to get a total charge of \(1\)on the other body?
1. \(200\) years
2. \(100\) years
3. \(150\) years
4. \(250\) years

Subtopic:  Electric Charge |
 58%
Level 3: 35%-60%
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The amount of positive and negative charges in a cup of water (\(250\) g) are respectively:

1. \(1.6 \times10^9\) C, \(1.4 \times10^9\) C
2. \(1.4 \times10^9\) C, \(1.6 \times10^9\) C
3. \(1.34 \times10^7\) C, \(1.34 \times10^7\) C
4. \(1.6 \times10^8\) C, \(1.6 \times10^7\) C
Subtopic:  Electric Charge |
 67%
Level 2: 60%+
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The ratio of the magnitude of electric force to the magnitude of gravitational force for an electron and a proton will be:
(\(m_p=1.67\times10^{-27}~\text{kg}\)\(m_e=9.11\times10^{-31}~\text{kg}\))
1. \(2.4\times10^{39}\)
2. \(2.6\times10^{36}\)
3. \(1.4\times10^{36}\)
4. \(1.6\times10^{39}\)

Subtopic:  Coulomb's Law |
 60%
Level 2: 60%+
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