Question

Two long, parallel conductors, separated by 14.0 cm, carry currents in the same direction. The first wire carries current I1 = 6.00 A, and the second carries I2 = 8.00 A Assume the conductors lie in the plane of the page.

(a) What is the magnitude of the magnetic field created by I1 at the location of I2?
T

(b) What is the force per unit length exerted on I2 by I1?
N/m

(c) What is the magnitude of the magnetic field created by I2 at the location of I1?
T

(d) What is the force per length exerted by I2 on I1?
N/m
direction

Answer 1

I₁=6A, I₂=8 A, b=0.14 m.
(a) B₁=μ₀I₁/2πb=4π•10⁻⁷•6/2π•0.14=8.57•10⁻⁶ T
(b)
F₂ =I₂B₁Lsinα
α=90° =>sinα=1
F₂/L =I₂B₁= =μ₀I₁I₂/2πb=8•8.57•10⁻⁶=6.86•10⁻⁵N/m
(c)
B₂=μ₀I₂/2πb=4π•10⁻⁷•8/2π•0.14=1.14•10⁻⁵ T
(d)
F₁ =I₁B₂Lsinα
α=90° =>sinα=1
F₁/L =I₁B₂=μ₀I₁I₂/2πb=
=6•1.14•10⁻ ⁵=6.86•10⁻⁵N/m
I₁↑ F₁→ ←F₂↑I₂