Magnetic forces?

Question

Two long, straight wires are separated by a distance of 32.7 cm. One wire carries a current of 2.69 A, the other carries a current of 4.33 A.

(a) Find the force per meter exerted on the 2.69 A wire.

Answer 1

F = ILB, and where I is the current in one wire, L is the length of that wire segment, and B is the magnetic field due to the other wire.

The B field of the other wire is B= µ₀I(/2πR), where R is the radial distance from the wire in meter.

Putting it together in mks units, F/L = µ₀ I1 I2 / (2πR)

F/L = (4π x 10^-7)(2.69)(4.33)/(2π 0.327)

=(2 x 10^-7)(2.69)(4.33)/(0.327)

=7.12 x 10^-6 N/m

Answer 2

Force per length is given by:

F / ℓ = µ₀I1I2 / 2πr

= ((4π x 10^-7 Tm/A) x 2.69 A x 4.33 A) / (2 x π x 0.327 m)

= 7.12 x 10^-6 N/m