The GATE Grind

GATE 2019 EC – Question 46

Electromagnetics · Maxwell's Equations · 2 marks · Multiple choice

Two identical copper wires W1 and W2, placed in parallel as shown in the figure, carry currents $I$ and $2I$, respectively, in opposite directions. If the two wires are separated by a distance of $4r$, then the magnitude of the magnetic field $\vec B$ between the wires at a distance $r$ from W1 is

Diagram for GATE 2019 EC question 46
  1. $\dfrac{\mu_0I}{6\pi r}$
  2. $\dfrac{6\mu_0I}{5\pi r}$
  3. $\dfrac{5\mu_0I}{6\pi r}$
  4. $\dfrac{\mu_0^2I^2}{2\pi r^2}$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) $\dfrac{5\mu_0I}{6\pi r}$

Explanation

The point is at distance $r$ from W1 and $3r$ from W2. Between opposite currents the two fields point the same way and add: $B=\frac{\mu_0I}{2\pi r}+\frac{\mu_0(2I)}{2\pi(3r)}=\frac{\mu_0I}{2\pi r}\left(1+\frac23\right)=\frac{5\mu_0I}{6\pi r}$.