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. μo = 4π x 10−7 Wb A−1 m−1.

Known :Magnetic field produced by two parallel current-carrying wires - problems and solutions 1

Electric current (I) = 3-A

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

Distance between wire 1 and P (r1P) = 30 cm = 0.3 m

Distance between wire 2 and P (r2P) = 40 – 30 = 10 cm = 0.1 m

µo = 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 two parallel current-carrying wires - problems and solutions 2

Magnetic field produced by wire 2 (right) :

Magnetic field produced by two parallel current-carrying wires - problems and solutions 3

Magnetic field at point P :

BP = B2 – B1 = 6 x 10-6 – 2 x 10-6

BP = 4 x 10-6 Tesla

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

Magnetic field produced by two parallel current-carrying wires - problems and solutions 4Known :

Electric current (I) = 2 A

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

μo = 4π x 10−7 Wb. A−1 m−1

Wanted : Magnitude and direction of magnetic induction at point P

Solution :

Magnetic field produced by two parallel current-carrying wires - problems and solutions 5

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