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GATE 2021 EE – Question 15

Engineering Mathematics · Calculus: Vector identities, Directional derivatives, Line integral, Surface integral, Volume integral, Stokes's theorem, Gauss's theorem, Divergence theorem, Green's theorem · 1 mark · Multiple choice

Which one of the following vector functions represents a magnetic field $\vec B$? ($\hat x$, $\hat y$, and $\hat z$ are unit vectors along x-axis, y-axis, and z-axis, respectively)

  1. $10x\hat x+20y\hat y-30z\hat z$
  2. $10y\hat x+20x\hat y-10z\hat z$
  3. $10z\hat x+20y\hat y-30x\hat z$
  4. $10x\hat x-30z\hat y+20y\hat z$

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Show answer and explanation

Correct answer: (A) $10x\hat x+20y\hat y-30z\hat z$

Explanation

A magnetic flux density must satisfy $\nabla\cdot\vec B=0$. For option A, $\nabla\cdot\vec B=10+20-30=0$. The divergences of B, C and D are $-10$, $20$ and $10$ respectively.