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GATE 2021 IN – Question 13

Electricity and Magnetism · Electrostatics and capacitance · 1 mark · Multiple choice

An infinitely long line with uniform positive charge density lies along the z-axis. In cylindrical coordinates $(r,\phi,z)$, the electric-field direction at a point off the z-axis is ______.

  1. $\hat r$
  2. $\hat\phi$
  3. $\hat z$
  4. $(\hat r+\hat z)/\sqrt2$

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Show answer and explanation

Correct answer: (A) $\hat r$

Explanation

Cylindrical symmetry makes the field independent of azimuth and excludes an axial component for an infinite uniform line. Gauss’s law gives E=λ/(2πεr) r̂. Positive charge points outward, hence **r̂, A**.