# 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 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 (r_{12}) = 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} = B_{2} – B_{1} = 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 :__