The electric field in a certain region is acting radially outward and is given by \(E=Ar.\) 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 |
 67%
From NCERT
NEET - 2015
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What is the flux through a cube of side \(a,\) if a point charge of \(q\) is placed at one of its corners?
1. \(\frac{2q}{\varepsilon_0}\)
2. \(\frac{q}{8\varepsilon_0}\)
3. \(\frac{q}{\varepsilon_0}\)
4. \(\frac{q}{2\varepsilon_0}\)

Subtopic:  Gauss's Law |
 88%
From NCERT
AIPMT - 2012
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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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The electric field at a distance \(\frac{3R}{2}\) from the centre of a charged conducting spherical shell of radius \(R\) is \(E\). The electric field at a distance \(\frac{R}{2}\) from the centre of the sphere is:
1. \(E\)
2. \(\frac{E}{2}\)
3. \(\frac{E}{3}\)
4. zero
 

Subtopic:  Gauss's Law |
 84%
From NCERT
AIPMT - 2010
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A hollow cylinder has a charge \(q\) coulomb within it (at the geometrical centre). If \(\phi\) 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. \(\frac{1}{2}\left(\frac{q}{\varepsilon_0}-\phi\right)\)
2. \(\frac{q}{2\varepsilon_0}\)
3. \(\frac{\phi}{3}\)
4. \(\frac{q}{\varepsilon_0}-\phi\)

Subtopic:  Gauss's Law |
 74%
From NCERT
AIPMT - 2007
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A square surface of side \(L\) (m) is in the plane of the paper. A uniform electric field \(\vec{E}\) (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 |
 81%
From NCERT
AIPMT - 2006
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