3 infinitely long thin wires each carrying current \( i \) in the same direction, are in the \( ...

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3 infinitely long thin wires each carrying current \( i \) in the same direction, are in the \( \mathrm{x}-\mathrm{y} \) plane of a gravity free space. The central wire is along the \( y \)-axis while the other two are along \( x=\pm d \).
(i) Find the locus of the points for which the magnetic field \( B \) is zero.
(ii) If the central wire is displaced along the z-direction by a small amount \& released, show that it will
\( \mathrm{P} \) execute simple harmonic motion. If the linear density of the wires is \( \lambda \), find the frequency of oscillation.
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