Magnetic force between two parallel wires – problems and solutions

1. Two parallel conductors carrying currents I₁ and I₂, as shown in the figure below. What is the magnitude and direction of the magnetic force experienced by both conductors? (μ_o = 4π. 10^-7 Wb.A^-1.m^-1)

Known :

The electric current 1 (I₁) = 3 Ampere

The electric current 2 (I₂) = 5 Ampere

The permeability of free space (µ_o) = 4π x 10^-7 wb A^-1 m^-1

Distance between both conductors (L) = 5 cm = 5 x 10^-2 meters

Wanted: The magnitude and direction of the magnetic force

Solution :

The direction of the electric current on conductor 1 is opposite with the direction of the electric current on conductor 2. Antiparallel currents (in opposite directions) exert a repulsive force on each other.

The magnitude of the magnetic force :

F/l = 6 x 10^-5 Newton

2. Two parallel wires carrying currents I₁ and I₂ are 20-cm apart. What is the magnitude of the magnetic force experienced by each wire (μ_o = 4π. 10^-7 Wb.A^-1.m^-1)

Known :

The electric current 1 (I₁) = 5 Ampere

The electric current 2 (I₂) = 4 Ampere

The permeability of free space (µ_o) = 4π x 10^-7 wb A^-1 m^-1

Distance between both wires (L) = 20 cm = 20 x 10^-2 meters

Wanted: The magnitude of the magnetic force

Solution :

The direction of the electric current on conductor 1 is opposite with the direction of the electric current on conductor 2. Antiparallel currents (in opposite directions) exert a repulsive force on each other.

The magnitude of the magnetic force :

F/l = 2 x 10^-5 Newton