Find electric field due to a uniformly charged, long and thin rod

[This question includes concepts from 12th syllabus]

1. kλr

2. kλ2r

3. 2kλr

4. kλ4r

Subtopic:  Electric Field | Gauss's Law |
 80%
From NCERT
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A hollow metal sphere of radius \(R\) is uniformly charged. The electric field due to the sphere at a distance \(r\) from the centre:

1. decreases as \(r\) increases for \(r<R\) and for \(r>R\).
2. increases as \(r\) increases for \(r<R\) and for \(r>R\).
3. zero as \(r\) increases for \(r<R\), decreases as \(r\) increases for \(r>R\).
4. zero as \(r\) increases for \(r<R\), increases as \(r\) increases for \(r>R\).
Subtopic:  Electric Field |
 75%
From NCERT
NEET - 2019
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Two point charges \(A\) and \(B\), having charges \(+Q\) and \(-Q\) respectively, are placed at a certain distance apart and the force acting between them is \(F.\) If \(25\%\) charge of \(A\) is transferred to \(B\), then the force between the charges becomes:

1. \(\frac{4F}{3}\) 2. \(F\)
3. \(\frac{9F}{16}\) 4. \(\frac{16F}{9}\)
Subtopic:  Coulomb's Law |
 76%
From NCERT
NEET - 2019
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Two parallel infinite line charges with linear charge densities \(+\lambda\) C/m and \(+\lambda\) C/m are placed at a distance \({R}.\) The electric field mid-way between the two line charges is:
1. \(\frac{\lambda}{2 \pi \varepsilon_0 {R}} \) N/C
2. zero
3. \(\frac{2\lambda}{ \pi \varepsilon_0 {R}} \) N/C
4. \(\frac{\lambda}{ \pi \varepsilon_0 {R}}\) N/C

Subtopic:  Gauss's Law |
 63%
From NCERT
NEET - 2019
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A hollow cylinder has a charge q coulomb within it (at the geometrical centre). If ϕ is the electric flux in units of Volt-meter associated with the curved surface B, the flux linked with the plane surface A in units of volt-meter will be: 
    

1. 12qε0-Φ


2. q2ε0


3. Φ3


4. qε0-Φ

Subtopic:  Gauss's Law |
 75%
From NCERT
AIPMT - 2007
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Three-point charges + q, -2q and +q are placed at points (x=0, y=a, z=0), (x=0, y=0, z=0) and (x=a, y=0, z=0), respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are:
 

1. 2qa along +y direction
2. 2qa along the line joining points (x=0, y= 0, z=0) and (x=a, y=a, z=0)
3. qa along the line joining points (x=0, y=0, z=0) and (x=a, y=a, z=0)
4. 2qa along +x direction
Subtopic:  Electric Dipole |
 84%
From NCERT
AIPMT - 2007
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A thin conducting ring of radius \(R\) is given a charge \(+Q.\) The electric field at the centre O of the ring due to the charge on the part AKB of the ring is \(E.\) The electric field at the centre due to the charge on the part ACDB of the ring is:

                      

1. \(3E\) along KO
2. \(E\) along OK
3. \(E\) along KO
4. \(3E\) along OK

Subtopic:  Electric Field |
 76%
From NCERT
AIPMT - 2008
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The mean free path of electrons in a metal is \(4\times 10^{-8}~\text{m}\). The electric field which can give an average of \(2~\text{eV}\) energy to an electron in the metal will be in units of Vm-1:
1. \(8\times 10^{7}\)
2. \(5\times 10^{-11}\)
3. \(8\times 10^{-11}\)
4. \(5\times 10^{7}\)
Subtopic:  Electric Field |
From NCERT
AIPMT - 2009
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A charge Q is enclosed by a Gaussian spherical surface of radius R. If the radius is doubled, then the outward electric flux will:
1. be reduced to half
2. remain the same
3. be doubled
4. increase four times
Subtopic:  Gauss's Law |
 88%
From NCERT
AIPMT - 2011
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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. \(\frac{r}{\sqrt[3]{2}}\)
2. \(\frac{r}{\sqrt[2]{2}}\)
3. \(\frac{2r}{3}\)
4. none of the above

Subtopic:  Coulomb's Law |
 70%
From NCERT
AIPMT - 2013
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