Q.
Two parallel long straight conductors are placed at right angle to the meter scale at the 2 cm and 6 cm marks as shown in the figure. If they carry currents $i\ and\ 3\ i$ respectively in the same direction, then they will produce zero magnetic field at
A) Zero mark
B) 9 cm mark
C) 3 cm mark
D) 7 cm mark
Explanation
(c) Distance between two linear conductor = 6-2= 4 cm. Let the distance of the point on scale from conductor carrying current $i\ be\ x$ cm where resultant magnetic field is zero. Then the distance of this point from other conductor is $(4 - x)$ cm. As per question
$\frac{\mu_{0}}{4\pi}\ \frac{2i}{r \times 10^{- 2}} = \ \frac{\mu_{0}}{4\pi}\ \frac{2(3i)}{(4 - x) \times 10^{- 2}}$
Or $3x = 4 - x - x\ \ or\ x = 1\ cm.$
$\therefore\ \ $Location of point on scale $= 2 + 1 = 3$ cm mark.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.