Gauss Theorem

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Question
ICSEENIPH12030027

State Gauss’s theorem.

Solution

Gauss’s theorem : It states that the electric flux fE, through any closed surface is 1/Î0 times the total charge q enclosed by the surface.
Mathematically, 
straight ϕ subscript straight E space equals space straight E with rightwards harpoon with barb upwards on top space. space ds with rightwards harpoon with barb upwards on top space equals space straight q over straight epsilon subscript straight o

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Question
ICSEENIPH12030094

An infinite line charge produces a field of 9 x 104 NC-1 at a distance of 2 cm. Calculate the linear charge density.   

Solution

For infinite long line charge,
straight E space equals space fraction numerator straight lambda over denominator 2 πε subscript straight o straight r end fraction space equals space fraction numerator 2 straight lambda over denominator 4 πε subscript straight o straight r end fraction

straight lambda space equals space linear space charge space density

straight r space equals space distance 
We have, 

E = 9 x io4 N/C

r = 2 cm = 2 x 10-2 m
Hence, 
9 space straight x space 10 to the power of 4 space equals space fraction numerator 2 space straight x space straight lambda space straight x space 9 space straight x space 10 to the power of 9 over denominator 2 space straight x space 10 to the power of negative 2 end exponent end fraction space

space space space space space space space space space space straight lambda space equals space 10 to the power of 4 over 10 to the power of 11 space equals space 10 to the power of negative 7 space end exponent cm 

Question
ICSEENIPH12030237

A short electric dipole (consists of two point charges +q and -q) is placed at the centre O and inside a large cube (ABCDEFGH) of length L, as shown in the figure below. The electric flux, remaining through the cube is:

  • fraction numerator straight q over denominator 4 πε subscript straight o straight L end fraction
  • Zero

  • fraction numerator straight q over denominator 2 πε subscript straight o straight L end fraction
  • fraction numerator straight q over denominator 3 πε subscript straight o straight L end fraction

Solution

B.

Zero

Since, it is an electric dipole, the net charge enclosed by the surface is zero. Therefore, according to Gauss's law, electric flux through the cube will be zero.