There are two wires lying on the plane of this page carry equal current to the same direction as shown. at a point midway between the wire, the magnetic field is
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To determine the magnetic field at the midpoint between the two wires, you can use the Biot-Savart Law. This law states that the magnetic field at a point due to a current-carrying wire is directly proportional to the current and inversely proportional to the distance from the wire.
Let's assume that the current flowing through each wire is I, and the distance between the two wires is d. At the midpoint between the wires, the distance from each wire is d/2.
Using the Biot-Savart Law, the magnetic field at the midpoint between the wires (B_midpoint) can be calculated for each wire:
B_midpoint = (μ₀ / 4π) * (I / (d/2))
where:
- μ₀ is the permeability of free space, approximately 4π × 10⁻⁷ Tm/A,
- I is the current flowing through each wire, and
- d/2 is the distance from each wire to the midpoint.
Since both wires are carrying equal currents in the same direction, the magnetic fields produced by each wire at the midpoint will add up.
Therefore, to calculate the magnetic field at the midpoint, you can simply double the magnetic field produced by one wire:
B_total = 2 * B_midpoint
Substituting B_midpoint into the equation, we get:
B_total = 2 * (μ₀ / 4π) * (I / (d/2))
Simplifying further, the equation becomes:
B_total = (μ₀ * I) / (2π * d)
So, the magnetic field at the midpoint of the wires is given by the equation above.