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Flux of Electric Field


The electric flux passing through an area $\vec{A}$ in an electric field $\vec{E}$ is given by \begin{align} \phi=\vec{E}\cdot\vec{A}. \end{align}

Problems from IIT JEE

Problem (IIT JEE 2011): Consider an electric field $\vec{E}=E_{0}\,\hat\imath$, where $E_0$ is a constant. The flux through the shaded region (as shown in figure) due to this field is,

  1. $2E_{0}a^2$
  2. $\sqrt{2}E_{0}a^2$
  3. $E_{0}a^2$
  4. $\frac{E_{0}a^2}{2}$

Solution: The flux through area vector $\vec{S}$ due to an electric field $\vec{E}$ is, \begin{align} \phi &=\oint\vec{E}\cdot\mathrm{d}\vec{S} \\ &=\vec{E}\cdot\oint\mathrm{d}\vec{S} \\ &=\vec{E}\cdot\vec{S}. \quad \text{(since $\vec{E}$ is constant.)} \end{align} The area vector of shaded region is cross product of vectors representing two sides i.e., \begin{align} \vec{S} & =(a\,\hat\jmath)\times(a\,\hat\imath+a\hat{k}) \\ &=a^2\,(\hat\imath-\hat{k}). \end{align} Use above equations to get, \begin{align} \phi &=(E_0\,\hat\imath)\cdot a^2\,(\hat\imath-\hat{k}) \\ &=E_0 a^2.\nonumber \end{align}


An uncharged spherical conductor of radius $R$ is placed in a non-uniform electric field (see figure). The electric flux through the sphere is (i) less than zero (ii) zero or (iii) greater than zero?



  1. Electric field
  2. Electric field lines
  3. Gauss's law and its application
JEE Physics Solved Problems in Mechanics