A charged ball \(B\) hangs from a silk thread \(S,\) which makes an angle \(\theta\) with a large charged conducting sheet \(P,\) as shown in the figure. The surface charge density \(\sigma\) of the sheet is proportional to: 

1. \(\sin\theta\)

2. \(\tan\theta\)

3. \(\cos\theta\)

4. \(\cot\theta\)

Subtopic:  Electric Field |
 62%
From NCERT
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Two-point charges +8q and –2q are located at x = 0 and x = L respectively. The location of a point on the x-axis at which the net electric field due to these two point charges is zero is 

1. 8 L

2. 4 L

3. 2 L

4. L4

Subtopic:  Electric Field |
 72%
From NCERT
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Three infinitely long charge sheets are placed as shown in the figure. The electric field at point P is 

(1) 2σεok^

(2) 2σεok^

(3) 4σεok^

(4) -4σεok^

Subtopic:  Electric Field |
 70%
From NCERT
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Two infinitely long parallel conducting plates having surface charge densities \(+\sigma\) and \(-\sigma\) respectively, are separated by a small distance. The medium between the plates is a vacuum. If \(\varepsilon_0\) is the dielectric permittivity of vacuum, then the electric field in the region between the plates is:
1. \(0~\text{V/m}\)
2. \(\frac{\sigma}{2\varepsilon_0}~\text{V/m}\)
3. \(\frac{\sigma}{\varepsilon_0}~\text{V/m}\)
4. \(\frac{2\sigma}{\varepsilon_0}~\text{V/m}\)
Subtopic:  Electric Field |
 60%
From NCERT
AIIMS - 2005
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Four-point +ve charges of the same magnitude (Q) are placed at four corners of a rigid square frame as shown in the figure. The plane of the frame is perpendicular to Z-axis. If a –ve point charge is placed at a distance z away from the above frame (z<<L) then 

1. – ve charge oscillates along the Z-axis.

2. It moves away from the frame.

3. It moves slowly towards the frame and stays in the plane of the frame.

4. It passes through the frame only once.

Subtopic:  Coulomb's Law |
 58%
From NCERT
AIIMS - 2005
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A cylinder of radius R and length L is placed in a uniform electric field E parallel to the cylinder axis. The total flux for the surface of the cylinder is given by 

(1) 2πR2E

(2) πR2/E

(3) (πR2πR)/E 

(4) Zero

Subtopic:  Gauss's Law |
 71%
From NCERT
PMT - 1975
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Electric field at a point varies as r0 for

(1) An electric dipole

(2) A point charge

(3) A plane infinite sheet of charge

(4) A line charge of infinite length

Subtopic:  Electric Field |
 69%
From NCERT
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Total electric flux coming out of a unit positive charge put in air is 

(1) ε0

(2) ε01

(3) (4pε0)1

(4) 4πε0 

Subtopic:  Gauss's Law |
 80%
From NCERT
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A cube of side l is placed in a uniform field E, where E=Ei^. The net electric flux through the cube is

(1) Zero

(2) l2E

(3) 4l2E

(4) 6l2E

Subtopic:  Gauss's Law |
 74%
From NCERT
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Eight dipoles of charges of magnitude \((e)\) are placed inside a cube. The total electric flux coming out of the cube will be: 
1. \(\frac{8e}{\epsilon _{0}}\)
2. \(\frac{16e}{\epsilon _{0}}\)
3. \(\frac{e}{\epsilon _{0}}\)
4. zero

Subtopic:  Electric Dipole |
 76%
From NCERT
PMT - 1998
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