Question

When$d$ $\approx$ a but wires are not touching the loop, it is found that the net magnetic field on the axis of the loop is zero at a height $h$ above the loop. In that case :

• A. Current in wire 1 and wire 2 is in the direction PQ and RS, respectively such $h\approx a$
• B. Current in wire 1 and wire 2 is in the direction PQ and SR, respectively and $h\approx a$
• C. Current in wire 1 and wire 2 is in the direction PQ and SR, respectively and $h\approx 1.2a$
• D. Current in wire 1 and wire 2 is in the direction PQ and RS, respectively and $h\approx 1.2a$

Answer 1

The correct option is C Current in wire 1 and wire 2 is in the direction PQ and SR, respectively and $h\approx 1.2a$

The net magnetic field at the given point will be zero if.
$|{\overrightarrow{B}}_{wires}|=|{\overrightarrow{B}}_{loop}|$
$2B_w\cos \theta =B_l$
$\Rightarrow 2\frac{{\mu }_{0}I}{2\pi \sqrt{a^2+h^2}}\times \frac{a}{\sqrt{a^2+h^2}}=\frac{{\mu }_{0}I{a}^2}{2(a^2+h^2{)}^{3/2}}$
$\Rightarrow h\approx 1.2a$

The direction of magnetic field at the given point due to the loop is normally out of the plane. Therefore, the net magnetic field due to the both wires should be into the plane. For this current in wire 1 should be along PQ and that in wire 2 should be along SR.