Question

A circular loop of radius r carries a current i. How should a long, straight wire carrying a current 4i be placed in the plane of the circle so that the magnetic field at the centre becomes zero?

Answer 1

Explanation:

Step 1:

Given Data in the question  

Current Magnitude = i

Loop Radius = r

Step 2:

Magnetic field due to the centering loop,

$B_{l}=\frac{\mu_{0} i}{2 r}$

Let a straight wire carrying 4i current be positioned at a distance x from the center so that the loop and The magnetic fields of the wire are of the same magnitude but in the opposite direction at O.

Step 3:

Magnetic field due to the wire in the loop's middle,

$B_{w}=\frac{\mu_{0} 4 i}{2 \pi x}$

Based on the question,

$B_{l}=B_{W}$

$\frac{\mu_{0} i}{2 r}=\frac{\mu_{0} 4 i}{2 \pi x}$

  $x=\frac{8 r}{2 \pi}$

     $=\frac{4 r}{\pi}$

Which means the wire is mounted $\frac{4 r}{\pi}$ from the loop center .

Answer 2

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