Magnetic field produced by two parallel current-carrying wires – problems and solutions

1. Two long parallel wires carrying the same currents, 3-A. If the distance between both wires is 40 cm, determine the magnetic field at point P. μ_o = 4π x 10⁻⁷ Wb A⁻¹ m⁻¹.

Known :

Electric current (I) = 3-A

Distance between wire 1 and 2 (r₁₂) = 40 cm = 0.4 m

Distance between wire 1 and P (r_1P) = 30 cm = 0.3 m

Distance between wire 2 and P (r_2P) = 40 – 30 = 10 cm = 0.1 m

µ_o = 4π x 10^-7 Wb.A^-1.m^-1

Wanted : Magnetic field at point P

Solution :

Magnetic field produced by wire 1 (left) :

Magnetic field produced by wire 2 (right) :

Magnetic field at point P :

B_P = B₂ – B₁ = 6 x 10^-6 – 2 x 10^-6

B_P = 4 x 10^-6 Tesla

2. A long wire carrying current 2-A. Determine magnitude and direction of magnetic field at point P. (μ_o = 4π x 10⁻⁷ Wb A⁻¹ m⁻¹)

Known :

Electric current (I) = 2 A

Distance between wire and point P (r_P) = 4 cm = 0.04 m

μ_o = 4π x 10⁻⁷ Wb. A⁻¹ m⁻¹

Wanted : Magnitude and direction of magnetic induction at point P

Solution :