Two long parallel wires are at a distance of 4 cm4 cm. They carry currents I𝐼 and 3I3𝐼 in same direction. Where will the field produced by both wires be zero from current I𝐼?

The magnetic field produced by a current-carrying wire at a distance r is given by Ampere's law as B = μ0I/2πr, where μ0 is the permeability of free space, I is the current, and r is the distance from the wire.

The magnetic field at a point due to both wires will be zero if the fields produced by them at that point are equal and opposite.

Let's consider two cases:

1. The point is between the wires: In this case, the field due to the wire carrying current I will be towards this wire and the field due to the wire carrying current 3I will be away from this wire. For the fields to be equal, we have μ0I/2πr = μ03I/2π(4-r), where r is the distance of the point from the wire carrying current I. Solving this equation gives r = 1 cm.

2. The point is outside the wires: In this case, the field due to both wires will be in the same direction. For the fields to be equal, we have μ0I/2πr = μ03I/2π(r-4), where r is the distance of the point from the wire carrying current I. Solving this equation gives r = 6 cm.

So, the field produced by both wires will be zero at 1 cm from the wire carrying current I between the wires and at 6 cm from the wire carrying current I outside the wires.