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GATE 2015 EC – Question 34

Electromagnetics · Maxwell's Equations · 1 mark · Multiple choice

Consider a straight, infinitely long, current carrying conductor lying on the $z$-axis. Which one of the following plots (in linear scale) qualitatively represents the dependence of $H_\phi$ on $r$, where $H_\phi$ is the magnitude of the azimuthal component of magnetic field outside the conductor and $r$ is the radial distance from the conductor?

Four plots of $H_\phi$ against $r$. (A) a horizontal line. (B) a straight line falling with $r$. (C) a curve that falls steeply and flattens out. (D) a curve that is flat at first and then drops sharply.
  1. Plot (A), a constant
  2. Plot (B), a straight falling line
  3. Plot (C), a curve falling as $\frac{1}{r}$
  4. Plot (D), a curve that drops sharply at large $r$

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Correct answer: (C) Plot (C), a curve falling as $\frac{1}{r}$

Explanation

By Ampere's law, $H_\phi = \frac{I}{2\pi r}$ outside the conductor. This falls off as $\frac{1}{r}$, steeply near the conductor and more slowly farther away, which is plot (C).