Question

Determine the magnitude of the force between two parallel wires.

Express your answer to two significant figures and include the appropriate units.

Answer 1

shown in figure above ::

two long straight parallel wires separated by a distance d carrying currents I₁ & I₂ respectively.

where, current flows in same direction

magnetic field on wire 1, B₁ = ?₀ I₁ / 2 d                      { equation 1 }

force on wire 2, F = B₁ I₂ L

F = ?₀ I₁ I₂ L / 2 d                     ( from 1 )

or F / L = ?₀ I₁ I₂ / 2 d                                                 { equation 2 }

where F / L = force per unit length

The direction of F₂ indicated shows that wire 2 will be attracted towards wire 1. In a similar manner, one can show that wire 1 will experience a force due to the magnetic field B₂ of wire 2, and this force F₁ will have a magnitude equal to that of F₂ given in Eq.(2) but opposite in direction. Thus, wire 1 will be attracted towards wire 2.

magnitude of the force between two parallel wires is given as ::

F = ?₀ I₁ I₂ L / 2 d    

If two long parallel wires (d = 1 m) apart each carry a current of ( I = 1 A),

F / L = ?₀ I₁ I₂ / 2 d = (4 x 10^-7) (1) (1) / 2 (1) = 2 x 10^-7 N/m

then the force per unit length on each wire is 2 x 10^{- 7} N/m.

suppose, length of the wire L = 45 m

distance between a two wire 1 & 2 , d = 8.8 cm = 8.8 x 10^-2 m

current flowing through a wire, I = 49 A

using an equation,

F = ?₀ I₁ I₂ L / 2 d                                                    ( since, I₁ = I₂ = I )

inserting all these values in above equation

F = (4 x 10^-7) (49 A )² (45 m ) / 2 (8.8 x 10^-2 m)

F = 0.25 N