Three infinitely long thin wires, each carrying current i in the same dieretion, are the xy plane of a gravity free space. The central wire is along the y-axis while the other two are along `x=+-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 and released, show that it will execute simple harmonic motion. If the linear mass density of the wires is `lamda`, find the frequency of oscillation.

Explanation

To solve the given problem step by step, we will break it down into two parts as specified in the question.

### Part (i): Finding the locus of points where the magnetic field \( B \) is zero

1. **Understanding the Setup**:
- We have three infinitely long wires carrying current \( I \) in the same direction.
- The central wire is along the y-axis, while the other two wires are located at \( x = +d \) and \( x = -d \).

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