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GATE 2014 EE (EE1) – Question 42

Electromagnetic Fields · Coulomb's Law, Electric Field Intensity, Electric Flux Density, Gauss's Law, Divergence · 2 marks · Multiple choice

Which Cartesian vector field cannot be magnetic flux density?

  1. $y^2\hat a_x+z^2\hat a_y+x^2\hat a_z$
  2. $z^2\hat a_x+x^2\hat a_y+y^2\hat a_z$
  3. $x^2\hat a_x+y^2\hat a_y+z^2\hat a_z$
  4. $y^2z^2\hat a_x+x^2z^2\hat a_y+x^2y^2\hat a_z$

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Correct answer: (C) $x^2\hat a_x+y^2\hat a_y+z^2\hat a_z$

Explanation

Magnetic flux density must satisfy∇·B=0because there are no magnetic monopoles. For **C**, B=(x²,y²,z²), the divergence is2x+2y+2z, not identically zero. In the other choices each component is independent of its own coordinate, giving zero divergence.