Two parallel wires carry currents in the same direction. I1=3A and I2=1A and the distance between the conductors is 4 cm. The magnetic field midway between these two wires is
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f/1=u.l1l2/2πd
f=4π*10^-7/2π*4
f=4*10^-7/8
f=5*10^-8N
To calculate the magnetic field midway between two parallel wires carrying currents in the same direction, we can use the Biot-Savart law. The Biot-Savart law states that the magnetic field (B) at a point due to a current in a wire is directly proportional to the current (I), the length of the wire segment (dl), and inversely proportional to the square of the distance (r) from the wire to the point.
The formula for the magnetic field at a point between two parallel wires is:
B = μ₀ * (I₁ * dl₁ / (2π * r₁)) - μ₀ * (I₂ * dl₂ / (2π * r₂))
Here, B is the magnetic field, μ₀ is the magnetic constant (4π × 10^(-7) T⋅m/A), I₁ and I₂ are the currents in the wires, dl₁ and dl₂ are the differential lengths of the wire segments, and r₁ and r₂ are the distances from the wires to the point where we want to calculate the magnetic field.
In this case, the wires are carrying currents in the same direction, so I₁ = 3A and I₂ = 1A. The distance between the conductors is given as 4 cm, which is equivalent to 0.04 m. Since the wires are parallel, the distances from the wires to the point midway between them will be the same.
Therefore, we can simplify the formula as:
B = μ₀ * [(I₁ * dl₁) / (2π * r₁) - (I₂ * dl₂) / (2π * r₁)]
Since we are interested in the magnetic field midway between the wires, we can assume that the lengths of the wire segments are the same and cancel them out.
B = μ₀ * [(I₁ - I₂) / (2π * r₁)]
Now, we can substitute the known values into the equation to find the magnetic field.
B = (4π × 10^(-7) T⋅m/A) * [(3 A - 1 A) / (2π * 0.04 m)]
Simplifying further:
B = (4π × 10^(-7) T⋅m/A) * ([2 A] / (2π * 0.04 m))
B = (4π × 10^(-7) T⋅m/A) * (1 / 0.04)
B = (4π × 10^(-7) T⋅m/A) * (25)
B = 100π × 10^(-7) T⋅m/A
Approximating using π ≈ 3.14 gives:
B ≈ 314 × 10^(-7) T⋅m/A
Therefore, the magnetic field midway between the two wires carrying currents in the same direction is approximately 314 × 10^(-7) T⋅m/A.