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GATE 2014 EE (EE2) – Question 42

Electromagnetic Fields · Biot-Savart law, Ampere law, Curl, Faraday law, Lorentz force · 2 marks · Multiple choice

An infinite wire carrying I A produces $|\mathbf B|=\mu_0I/(2\pi d)$ at perpendicular distance d m. One wire lies on the x-axis carrying 4 A in +x; another lies on the y-axis carrying 2 A in +y. In a right-handed Cartesian system, find magnetic field intensity H at (2,1,0).

Diagram for GATE 2014 EE (EE2) question 42
  1. $\frac3{2\pi}\hat k$ Wb/m²
  2. $\frac4{3\pi}\hat i$ A/m
  3. $\frac3{2\pi}\hat k$ A/m
  4. $0$ A/m

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Show answer and explanation

Correct answer: (C) $\frac3{2\pi}\hat k$ A/m

Explanation

For the+xwire,the perpendicular distance is1m and the right-hand rule gives+zfield Hx=4/(2π)k. For the+ywire,the distance is2m and the field is−z,Hy=−2/(4π)k. Their sum is **3/(2π)k A/m,C**. The question asks H,so do not multiply by free-space permeability or use B units.