The unit of current, the ampere, is defined in terms of the force between currents. Two 1.0-meter-long sections of very long wires a distance 5.0 mm apart each carry a current of 1.0 AA. What is the force between them? (If the force between two actual wires has this value, the current is defined to be exactly 1 A.)

(4 × 10⁻⁵) N

Explanation:

Magnetic force between two current carrying wires is given as

(F/L) = (μ₀I₁I₂)/2πr

where (F/L) = Force per unit length

L = Length of the wire section = 1 m

μ₀ = magnetic constant = (4π × 10⁻⁷) H/m

I₁ = Current in wire 1 = 1.00 A

I₂ = Current in wire 2 = 1.00 A

r = distance between the wires = 5.00 mm = 0.005 m

(F/L) = (μ₀I₁I₂)/2πr

(F/L) = [(4π × 10⁻⁷ × 1 × 1)/(2π × 0.005)]

(F/L) = 0.00004 N/m

F = 0.00004 × 1 = 0.00004 N = (4 × 10⁻⁵) N

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