Three long parallel wires carry currents as shown:

• Left wire = 3 A upward
• Middle wire = 1 A downward
• Right wire = 2 A downward

Distance between left and middle wire = 3 cm

Distance between middle and right wire = 2 cm

Find the force on 15 cm length of the middle wire.

Solution:

Force between parallel wires:

F = μ₀I₁I₂L / 2πd

Force due to left wire:

F₁ = (4π×10⁻⁷ × 3 × 1 × 0.15) / (2π × 0.03)

F₁ = 3 × 10⁻⁶ N

Force due to right wire:

F₂ = (4π×10⁻⁷ × 2 × 1 × 0.15) / (2π × 0.02)

F₂ = 3 × 10⁻⁶ N

Total force:

F = F₁ + F₂

= 6 × 10⁻⁶ N

= 6 μN

Answer: 6 μN